Skip to main content

Beginning Activity Beginning Activity 2: Proving that Statements Are Equivalent
A4US

1.

Let X, Y, and Z be statements. Complete a truth table for [(X→Y)∧(Y→Z)]→(X→Z).

2.

Assume that P, Q, and R are statements and that we have proven that the following conditional statements are true:

  • If P then Q (P→Q).

  • If Q then R (Q→R).

  • If R then P (R→P).

Explain why each of the following statements is true.

(a)

P if and only if Q (P↔Q).

(b)

Q if and only if R (Q↔R).

(c)

R if and only if P (R↔P).

Remember that X↔Y is logically equivalent to (X→Y)∧(Y→X).