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It develops the power to apply logic and logic is an intigral part of mathematics. More over application of venn diagrams helps to get solutions of complicated questions easily. Set theory is a combination of art, logic and calculations.
formal is just study of logic with purely formal content and material is the branch of logic that focuses the content of reasoning.
Boolean Algebra is the study of the algebra of logic whilst Mathematical logic is a way of applying Boolean algebra. Other applications include set theory, digital logic and probability.
Logic is important in computing as it is part of computer language and without it, mathematics in the computer will be impossible.
Because computers uses binary as its language. And programs are representation of logic.