Lecture 2 Symbolic Logic Worksheet With Answers Page 3

The conditional p→q, “if p then q” is called conditional (or an implication); p is called

the hypothesis (or premise) of the conditional, and q is called the conclusion of the (p

implies q).

Example 5: Using the symbolic representations

P: I am healthy

Q: I eat junk food.

R: I exercise regularly.

Express the following compound statements in symbolic form:

a. I am healthy if I exercise regularly.

b. If I eat junk food and do not exercise, then I am not healthy.

Solutions:

a. r→p

b. (q^~r) →(~p)

For the condition p→q, we say p is sufficient (condition) for q. And q is necessary

(condition) for p.

Example 6: on page 24

Express the following statements in symbolic form:

a. All mammals are warm-blooded.

b. No snake is warm-blooded.

p: It is a mammal.

q: It is warm-blooded.

p→q

p: It is a snake.

q: It is warm-blooded.

p→~q

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