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.
