Question

P: x – 5 =10 q: 4x + 1 = 61 Which is the inverse of p → q?

a- If x – 5 ≠ 10, then 4x + 1 ≠ 61.
b- If 4x + 1 ≠ 61, then x – 5 ≠ 10.
c-If x – 5 = 10, then 4x + 1 = 61.
d- If 4x + 1 = 61, then x – 5 = 10.

Answer 1

The inverse is b. If 4x+1 .NE. 61, then x-5 .NE.10

Answer 2

Answer: the correct option is

(a) If x – 5 ≠ 10, then 4x + 1 ≠ 61.

Step-by-step explanation: We are given to select the correct inverse of the conditional statement p → q if

p : x – 5 =10 and q : 4x + 1 = 61.

We know that

the inverse of a conditional statement p → q is given by "not p → not q".

Therefore, the inverse of the given statement is

not p → not q

that is, if x – 5 ≠ 10, then 4x + 1 ≠ 61.

Thus, the required inverse is " x – 5 ≠ 10, then 4x + 1 ≠ 61."

Option (a) is CORRECT.