Mathematics
Assertion (A) : The solution set in the system of negative integers for : 0 > -4 - p is {-3, -2. -1}.
Reason (R) : If the same quantity is subtracted from both sides of an equation, the symbol of inequality is reversed.
Both A and R are correct, and R is the correct explanation for A.
Both A and R are correct, and R is not the correct explanation for A.
A is true, but R is false.
A is false, but R is true.
Linear Inequations
1 Like
Answer
Given,
⇒ 0 > -4 - p
Adding 4 on both sides, we get :
⇒ 0 + 4 > -4 - p + 4
⇒ 4 > -p
⇒ -p < 4
⇒ p > -4 (Multiplying by a negative number reverses the inequality)
This inequality means p can be any real number greater than -4.
The solution set = {-3, -2, -1}.
So, assertion (A) is true.
As we know that adding or subtracting the same quantity from both sides of an inequality does not change the direction of the inequality symbol.
So, reason (R) is false.
∴ A is true, but R is false.
Hence, option 3 is the correct option.
Answered By
2 Likes
Related Questions
Assertion (A) : The solution set for :
x + 3 ≥ 15 is Φ, if the replacement set is {x | x < 10, x ∈ N}.
Reason (R) : If we change over the sides of an equality, we must change the sign from < to > or > to < or ≥ to ≤ or ≤ to ≥.
Both A and R are correct, and R is the correct explanation for A.
Both A and R are correct, and R is not the correct explanation for A.
A is true, but R is false.
A is false, but R is true.
Assertion (A) : x < -2 and x ≥ 1.
⇒ Solution set S = {x | -2 < x ≤ 1, x ∈ R}
Reason (R) : Two inequations can be written in a combined expression.
Both A and R are correct, and R is the correct explanation for A.
Both A and R are correct, and R is not the correct explanation for A.
A is true, but R is false.
A is false, but R is true.
If the replacement set is the set of natural numbers, solve:
(i) x - 5 < 0
(ii) x + 1 ≤ 7
(iii) 3x - 4 > 6
(iv) 4x + 1 ≥ 17
If the replacement set = {-6, -3, 0, 3, 6, 9}, find the truth set of the following:
(i) 2x - 1 > 9
(ii) 3x + 7 ≤ 1