Question

Determine whether these biconditionals are true or false.

a) 2+2 = 4 if and only if 1 +1 = 2.
b) 1+1 = 2 if and only if 2 + 3 = 4.
c) 1+1 = 3 if and only if monkeys can fly.
d) 0 > 1 if and only if 2 > 1.

Answer 1

b) a biconditional is true if and only if both statements on each side are true.

Step-by-step explanation:

To determine whether these biconditionals are true or false, we need to examine the statements on each side of the 'if and only if' connector.

1. For biconditional a), 2+2=4 is true and 1+1=2 is true, so the biconditional is true.
2. For biconditional b), 1+1=2 is true and 2+3=4 is false, so the biconditional is false.
3. For biconditional c), 1+1=3 is false and monkeys can't fly, so the biconditional is true because both statements are false.
4. For biconditional d), 0>1 is false and 2>1 is true, so the biconditional is false.