Statement I The set x: x is a real number and .x2-1=0 is the empty set. Statement II The set A= x: x ∈ R, x2=16. and 2 x=6 is an empty set.

Question

Statement I The set x: x is a real number and .x2-1=0 is the empty set. Statement II The set A= x: x ∈ R, x2=16. and 2 x=6 is an empty set. (A) Statement I is true (B) Statement II is true (C) Both are true (D) Both are false

Tardigrade Admin · Accepted Answer

The set of real numbers which satisfy x2-1=0, is -1,1 . So, Statement I is false. Given, x2=16 and 2 x=6 x=4,-4 text and x=3 ∴ There is no real x which simultaneously satisfied x2=16 and 2 x=6 So, Statement II is true.

Q. Statement I The set ${x : x$ is a real number and $x^{2} - 1 = 0}$ is the empty set.
Statement II The set $A = {x : x \in R, x^{2} = 16$ and $2 x = 6}$ is an empty set.

Statement I is true

Statement II is true

Both are true

Both are false

The set of real numbers which satisfy $x^{2} - 1 = 0$ , is ${- 1, 1}$ .
So, Statement $I$ is false.
Given, $x^{2} = 16$ and $2 x = 6$
$x = 4, - 4 and x = 3$
$∴$ There is no real $x$ which simultaneously satisfied $x^{2} = 16$ and $2 x = 6$
So, Statement II is true.

Q. Statement I The set {x:x is a real number and x2−1=0} is the empty set. Statement II The set A={x:x∈R,x2=16 and 2x=6} is an empty set.