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Question 41686

posted 11 months ago

Proposition: For neZ and n21, 6° -1 is divisible by 5.
Prove using mathematical induction the following proposition:

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Question 41684

posted 11 months ago

2.3. Prove by contradiction the following proposition:
Proposition: If a e Z and, if a? - 2a + 7 is even, then a is odd.

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Question 41680

posted 11 months ago

Prove using the laws of logic that
(-\mathrm{Q} \rightarrow-\mathrm{P}) \rightarrow(\mathrm{P} \rightarrow \mathrm{Q})=\text { True }

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Question 41677

posted 11 months ago

Use the truth tables method to determine whether
(\neg p \vee q) \wedge(q \rightarrow \neg r \wedge \neg p) \wedge(p \vee r) \text { is satisfiable }

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Question 41682

posted 11 months ago

. Prove (using a direct proof method) the following proposition:
Proposition: If a is an even integer number, then 7(a + 3) is odd.

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Question 41685

posted 11 months ago

Prove using mathematical induction that for all n 2 1,
1+4+7+\cdots+(3 n-2)=(n(3 n-1)) / 2

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Question 41678

posted 11 months ago

\text { Is the compound proposition } \neg(P \vee Q \vee R) \text { a contradiction? Justify. }

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Question 41679

posted 11 months ago

. Prove using the laws of logic that
A \rightarrow(B \vee C) \equiv(A \rightarrow B) \vee(A \rightarrow C)

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Question 41681

posted 11 months ago

5. Prove using the laws of logic that
(p \rightarrow r) \wedge(q \rightarrow r) \equiv((p \vee q) \rightarrow r)

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Question 41683

posted 11 months ago

2. Prove by contradiction the following proposition:
Proposition: For every n e z, then n? + 2 is not divisible by 4.

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