Question

To prove an iff statement A <=> B, we must prove:

a) A => B
b) A or B
c) A <= B
d) A <=> B

Answer 1

To prove an iff statement A ⇔ B, we must show both A ⇒ B and A ⇐ B, confirming the bi-directional relationship necessary for equivalence.

Step-by-step explanation:

To prove an iff statement A ⇔ B, we must prove both (a) A ⇒ B and (c) A ⇐ B. The statement ‘A or B’ is not sufficient for proving an equivalence; it doesn't establish the necessary bi-directional relationship between A and B. The correct answers are, therefore, both parts (a) and (c):

• (a) A ⇒ B: This shows that whenever A is true, B must also be true.
• (c) A ⇐ B: This demonstrates that whenever B is true, A must also be true.

By proving these two implications, we establish the bi-directional or two-way relationship required for A ⇔ B, meaning ‘A if and only if B’.