Mathematics
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.
Linear Inequations
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Answer
Given,
⇒ x + 3 ≥ 15
Subtracting by 3 on both sides, we get :
⇒ x + 3 - 3 ≥ 15 - 3
⇒ x ≥ 12
The replacement set = {x | x < 10, x ∈ N} = {1, 2, 3, 4, 5, 6, 7, 8, 9}
Since no elements of the replacement set satisfy the inequality,
∴ Solution set is Φ.
So, assertion (A) is true.
Let's suppose a and b are two real numbers, such that :
⇒ a < b
⇒ b > a
Thus, we can say that, if we change over the sides of an equality, we must change the sign from < to > or > to < or ≥ to ≤ or ≤ to ≥.
So, reason (R) is true.
∴ Both A and R are correct, and R is not the correct explanation for A.
Hence, option 2 is the correct option.
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Related Questions
Statement 1: A set from which the values of the variable involved in the inequation are chosen is called the solution set.
Statement 2: A linear inequation variable (or unknown) has exactly one solution.
Which of the following options is correct?
Both the statements are true.
Both the statements are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.
Assertion (A) : The solution set for :
x + 5 ≤ 10, if the replacement set is {x | x ≤ 5, x ∈ W} is {0, 1, 2, 3, 4, 5}.
Reason (R) : The set of elements of the replacement which satisfy the given inequation is called the solution set.
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.
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.