Hint :- * is not Commutative. How ? take (1,2), (3,4)EG.prove.

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A:

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Q: 7. Consider the operation a * b = a + b – ab on the set S = Z. a) Is this operation commutative?…

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Q: 3. Write the contrapositive of: Va eZ, if 6|a then 2|a and 3|a

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Q: 3.3. Let a, BEC. Prove that la + B2 + la – B|2 2(la|? + |B|?), and deduce that |a + Va? – B2|+ |la –…

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Q: Need a formal proof: Show: Let x,y ∈ R. Then | |y| - |x| | ≤ |y-x|. Hint:a = |x|, b=|y| and ε =…

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Q: Which of the following statement is/are TRUE.

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Q: Give the converse and contrapositive of: If 5 < 2 and 3 is odd, then 5 + 5 = 10. %3D

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Q: 5. All are examples of tautologies that are implications except A. (pa q) →p В. p - (pa 9) 9 - (pVq)…

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Q: What a n' 6) Σ-r 2" abso n=1 conver conditi

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A: False

Q: 3. Write the contrapositive of: VaeZ, if 6|a then 2| a and 3| a

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Q: Assume that Vxdy P (x, y) is false and that the domalh nonempty. Which of the following must also be…

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Q: Prove the statement: If n² is even then n is even. Hint: prove the contrapositive.

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Q: 8. What statement could be used to prove that m / n? O 42 6 O mZ1-m 22 = 180° O m23 - m = 180 0 2…

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Q: т F 13. If r + 123454321, then n# 11111. T F 15. The negation of an implication is another…

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A: converse of "If there is ice on the lake, then it is cold" is ? Converse means q--&gt;p

Q: Which one of the following statements is NOT TRUE

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