Kenneth Rosen Edition 6th Exercise 1.1 Question 12 (Page No. 17)

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

• A. 2 + 2 = 4 if and only if 1 + 1 = 2. = T <->T= True.
• B. 1 + 1 = 2 if and only if 2 + 3 = 4. = T<->F = False.
• C. 1 + 1 = 3 if and only if monkeys can fly.= F <-> F = True.
• D. 0 > 1 if and only if 2 > 1 = F<->T= False.

Comments

Option C should True instead of Not known.

The first statement (1+1=3) is False and the second statement (monkeys can fly) is also False, consequently making the bi-conditional True.