Question

5. Prove the conditional by proving the contrapositive:

Answer 1

Answer + Step-by-step explanation:

the conditional statement :

For two positive integers n and m,

nm = 4 ⇒  (n = 1  or  m = 1)  or  (n=m= 2)

the contrapositive:

(n ≠ 1  and  m ≠ 1)  and  (n ≠ 2 or m ≠ 2) ⇒ nm ≠ 4

Prove the conditional by proving the contrapositive :

Suppose

m ≠ 1

and m ≠ 2

and n ≠ 1

⇒ nm ≠ 1 × n  and  nm ≠ 2 × n  and n ≠ 1

⇒ nm ≠ 4  (because 4 = 4 × 1 or 4 = 2 × 2)

Conclusion:

The contrapositive is true then conditional is true.