Question

Assertion (A) The inequality $ax+by<0$ is strict inequality.
Reason (R) The inequality $ax+b\ge 0$ is slack inequality.

• A. Both $A$ and $R$ are correct; $R$ is the correct explanation of $A$
• B. Both A and R are correct: $R$ is not the correct explanation of $A$
• C. $A$ is correct; $R$ is incorrect
• D. $R$ is correct: $A$ is incorrect

Answer 1

Answer: (B)

Let us consider some inequalities
$ax+b<0$ ...(i)
$ax+b>0$ ...(ii)
$ax+b\le 0$ ...(iii)
$ax+b\ge 0$ ...(iv)
$ax+by>c$ ...(v)
$ax+by\le c$ ...(vi)
$a{x}^2+bx+c>0$ ...(vii)
$a{x}^2+bx+c\le 0$ ...(viii)
Inequalities (i), (ii), (v) and (vii) are strict inequalities, while inequalities (iii), (iv), (vi) and (viii) are slack inequalities.
$\therefore$ Both A and R are correct but R cannot explain A.