What is the negation of the following statement i

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Nature of Mathematics
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Chapter 3 / Exercise 24
Nature of Mathematics
Smith
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C. If n is divisible by both 2 and 3 then n is not divisible by 6. D. If n is not divisible by both 2 and 3 then n is not divisible by 6. E. If n is divisible by 6 then n is not divisible by both 2 and 3. F. If n is divisible by 6 then n is divisible by both 2 and 3. What is the contrapositive of the following: ”If P is a square then P is a rectangle.” A. If P is a square then P is not a rectangle. B. If P is a rectangle then P is a square. C. If P is a rectangle then P is not a square. D. If P is not a rectangle then P is not a square. E. If P is not a square then P is not a rectangle. F. If P is a square then P is a rectangle.
What is the negation of the following statement: ”I form a study group or I raise my grades.” A. I work alone and I raise my grades. B. I work alone or I raise my grades. C. I work alone or I lower my grades. D. I form a study group and I raise my grades. E. I form a study group and I lower my grades. F. I form a study group or I lower my grades. G. I work alone and I lower my grades. H. I form a study group or I raise my grades. What is the converse of the following: ”If this triangle has two 45 degree angles then it is a right triangle.” A. If this triangle does not have two 45 degree angles then it is not a right triangle. B. If it is not a right triangle then this triangle does not have two 45 degree angles. C. If it is a right triangle then this triangle has two 45 degree angles. D. If this triangle has two 45 degree angles then it is not a right triangle. E. If it is a right triangle then this triangle does not have two 45 degree angles. F. If this triangle has two 45 degree angles then it is a right triangle. What is the inverse of the following: ”If n is divisible by 6 then n is divisible by both 2 and 3.” A. If n is divisible by both 2 and 3 then n is divisible by 6. B. If n is not divisible by 6 then n is not divisible by both 2 and 3. 15. (1 point) For the following proof (of equivalence of 2 formulae) provide the justifications at each step, using the fol- lowing equivalences. Use the following key: a Idempotent Law b Double Negation c De Morgan’s Law d Commutative Properties e Associative Properties f Distributive Properties g Equivalence of Contrapositive h Definition of Implication i Definition of Equivalence j Identity Laws ( p F p T p ) k Tautology ( p ∨¬ p T ) l Contradiction ( p ∧¬ p F ) ¬ ( ¬ p q ) ( p q ) = ( ¬ ( ¬ p ) ∨¬ q ) ( p q ) by = ( p ∨¬ q ) ( p q ) by = p ( ¬ q q ) by = p ( q ∧¬ q ) by 9 Answer(s) submitted: (incorrect) Correct Answers: B J E G C B D
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Nature of Mathematics
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Chapter 3 / Exercise 24
Nature of Mathematics
Smith
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