명제와 조건 연습문제 — Sundstrom, Mathematical Reasoning · 1.1절 · 3d번

Sundstrom, Mathematical Reasoning · 1.1절 · 3d번영어 원문

Determine whether each of the following conditional statements is true or false.

If $7 \lt 10$ , then $3 + 5 =8$ .

정답·풀이 보기 (영어 원문)

This statement is true.

한 번 더 — 비슷한 문제Sundstrom, Mathematical Reasoning · 2.2절 · 7b번영어 원문

Use previously proven logical equivalencies to prove each of the following logical equivalencies about conditionals with conjunctions:

$\left[ {P \to \left( {Q \wedge R} \right)} \right] \equiv \left( {P \to Q} \right) \wedge \left( {P \to R} \right)$

다 풀었으면 정답 확인

In this case, we start with the left side.

$\begin{aligned}\left[ P \to \left( Q \wedge R \right) \right] & \equiv \neg P \vee \left( Q \wedge R \right) \\ & \equiv \left( \neg P \vee Q \right) \wedge \left( \neg P \vee R \right) \\ & \equiv \left( P \to Q \right) \wedge \left( P \to R \right)\end{aligned}$

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