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Geoffrey Hunter has written:
'Metalogic' -- subject(s): First order logic
'Waterloo Boy'
1 answer
The rules can be expressed in English as:
The negation of a conjunction is the disjunction of the negations.
The negation of a disjunction is the conjunction of the negations.
The rules can be expressed in formal-languagewith two propositions P and Q as:
where:
- ¬ is the negation operator (NOT)
- is the conjunction operator (AND)
- is the disjunction operator (OR)
- ⇔ is a metalogic-1symbol meaning "can be replaced in a formal-proofwith"
1 answer
with the doing of the hot sun you can survive in the savvannas in metalogic form.there is water in the center of every plant in the dessert and the savvannas!!!!!!!!!so in the few days all that you need is water for food you would have to eat lizards.the aftering of eating then attracts more food or meat and you shelter is a large piece of wood most likely and if you are lucky,a very large tree!!!!!!!!!!!!!!!!!!!
5 answers
1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 +
3 answers
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2 answers
152
1 answer
10 x 10=100. Would you rather go like this: 1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1=100?
12 answers
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 5
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 10
1 1 1 1 1 1 1 1 1 1 5 5 5
1 1 1 1 1 1 1 1 1 1 5 10
1 1 1 1 1 5 5 5 5
1 1 1 1 1 5 5 10
1 1 1 1 1 10 10
5 5 5 5 5
5 5 5 10
5 10 10
12 ways
2 answers
1+1+1+1+1+1+1+1+1+1+1+1+1=13 3 divided by 10 = 30
3 answers
I assume by "square numbers" you mean perfect squares.
You didn't say how many of each were allowed:
1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1²= 23
1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 2² = 23
1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 2² + 2² = 23
1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 3² = 23
1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 2² + 2² + 2² = 23
1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 2² + 3² = 23
1² + 1² + 1² + 1² + 1² + 1² + 1² + 2² + 2² + 2² + 2² = 23
1² + 1² + 1² + 1² + 1² + 1² + 1² + 4² = 23
1² + 1² + 1² + 1² + 1² + 3² + 3² = 23
1² + 1² + 1² + 2² + 2² + 2² + 2² + 2²= 23
1² + 1² + 1² + 2² + 4² = 23
1 answer
1+1+1+1+1+1+1+1+1+-1+1+1+10
1+1+1+1+1+1+1+1+1=9
1+1+1+1+1+1+1+1+1+-1=8
1+1+1+1+1+1+1+1+1+-1+1+1+10=20
1 answer
1 and 1 and 1 and 1 and 1 and 1 and 1 and 1 and 1 and 1
and 1 and 1 and 1 and 1 and 1 and 1 and 1 and 1 and 1 and 1
and 1 and 1 and 1 and 1 and 1 and 1 and 1 and 1 and 1 and 1
and 1 and 1 and 1 and 1 and 1 and 1 and 1 and 1 and 1 and 1
and 1 and 1 and 1 and 1 and 1 and 1.
Or
1.1 and 1.1 and 1.1 and 42.7
or an infinite number of other possibilities.
2 answers
(-1)3 = (-1)(-1)(-1) = -1
(-1)3 = (-1)(-1)(-1) = -1
(-1)3 = (-1)(-1)(-1) = -1
(-1)3 = (-1)(-1)(-1) = -1
3 answers
11111 x 11111 = 123454321
1 1 1 1 1
x 1 1 1 1 1
_______________
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
+ 1 1 1 1 1
_______________
1 2 3 4 5 4 3 2 1
1 answer
[Legend: Each number represents the denomination (amount) of the coin.]
1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1 = 25
1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+5 = 25
1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+5+5 = 25
1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+10 = 25
1+1+1+1+1+1+1+1+1+1+5+5+5 = 25
1+1+1+1+1+5+5+10 = 25
1+1+1+1+1+5+5+5+5 = 25
1+1+1+1+1+10+10 = 25
5+5+5+5+5 = 25
5+5+5+10 = 25
5+10+10 = 25
So the answer is 11!!!
I think you're missing 1+1+1+1+1+1+1+1+1+1+5+10 = 25 ?
1 answer
1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1 is one example.
1 answer
The answer is -1.
(1 + 1 x 1)/(1 - 1 x 1 -1) + 1 =
Follow the order of operations: parentheses/brackets, exponents, multiplication and division from left to right, and addition and subtraction from left to right.
Numerator:
Simplify 1 x 1 to 1.
(1 + 1)/(1 - 1 x 1 -1) + 1
Simplify 1 + 1 to 2.
2/(1 - 1 x 1 - 1) + 1
Denominator:
Simplify 1 x 1 to 1.
2/(1 - 1 - 1) + 1
Simplify 1 - 1 - 1 to -1.
2/(-1) +1
Simplify 2/(-1) to -2.
-2 +1
Simplify.
-1
4 answers
There are infinitely many possible solutions. One of them is
1 + 1 + 1 + 1 + 1 + 1 +1 + 1 + 1 + 1 +
1 + 1 + 1 + 1 + 1 + 1 +1 + 1 + 1 + 1 +
1 + 1 + 1 + 1 + 12
1 answer
They are -1 and +1.
They are -1 and +1.
They are -1 and +1.
They are -1 and +1.
2 answers
1 quarter, 2 dimes, 2 nickels, and 45 pennies
1+2+2+45=50
25+10+10+5+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1=100
1 answer
1 quarter, 2 dimes, 2 nickels, and 45 pennies.
1+2+2+45=50
25+10+10+5+5+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1
1 answer
The reciprocal of 1 is 1.
Proof:
a. 1*(1/1) = 1 because a*(1/a) = 1
b. 1*1 =1 because 1*a = a
c. 1/1 = 1 compare a. and b.
7 answers
There are infinitely many possible answers.
One such is 1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+16
1 answer
There are no two numbers that multiply to get 6 but add to get 18. In fact, the solutions are:
- 1x1x1x1x1x1x1x1x1x1x1x1x6 = 6; 1+1+1+1+1+1+1+1+1+1+1+1+6 = 18
- 1x1x1x1x1x1x1x1x1x1x1x1x1x2x3 = 6; 1+1+1+1+1+1+1+1+1+1+1+1+1+2+3 = 18
1 answer
1
1 answer
There are infinitely many possible answers:
One possible answer:
-1 and - 1 and - 1 and - 1 and - 1 and - 1 and - 1 and - 1
that is (-1) + (-1) + (-1) + (-1) + (-1) + (-1) + (-1) + (-1)
1 answer
1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 - 1 + 1 + 1 + 1 + 1 + 1 x 0
= (1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1) + (1 - 1) + (1 + 1 + 1 + 1) + (1 x 0)
= 9 + 0 + 4 + 0
= 13
It depends on if the entire equation is being multiplied by 0 or just the last plus 1. If it is just the last plus 1 then the answer is 13 like shown above. If the entire problem is being multiplied by 0 then the answer is 0.
1 answer
1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 11 - 9,999,999 = - 9,999,978
1 answer
you take 1 of the 1s and put it in the tenths place. Then you add the 1+1+1+1+1 and put the answer(5) in the ones place! that is how you get 15 out of 1 1 1 1 1 1.
1 answer
1+1+1+1+254
1+1+1+2+253
1+1+1+3+252
1+1+1+4+251
and
1*1*1*1*258
1 answer
