Given: p: x – 5 =10 q: 4x + 1 = 61 Which is the inverse of p → q? If x – 5 ≠ 10, then 4x + 1 ≠ 61. If 4x + 1 ≠ 61, then x – 5 ≠ 10. If x – 5 = 10, then 4x + 1 = 61. If 4x + 1 = 61, then x – 5 = 10.
Accepted Solution
A:
Answer: If x – 5 ≠ 10, then 4x + 1 ≠ 61
Justification:
1) The inverse of a conditional is negating both the hipothesis and the conclusion of the conditional, keeping the same sense of the implication.
2) This is the scheme (the symbol ~ is used to negate)
conditional: p → q hypothesis: p conclusion: q
negated hypothesis: ~p negated conclusion: ~ q
inverse conditional: ~p → ~q
3) So, for the hypotheis p: x – 5 =10 and the conclusion q: 4x + 1 = 61, the conditional p→ q is:
if x - 5 = 10 then 4x + 1 = 61.
And the inverse is negating both the x - 5 = 10 and 4x + 1 = 61, leading to:
If x – 5 ≠ 10, then 4x + 1 ≠ 61, which is the answer.