Let Z be the set of integers. If A = { x in Z | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Given $A = \{ x \in Z : 2^{(x + 2)(x^2 - 5x + 6)} = 1 \}$.Since $2^0 = 1$,we have $(x + 2)(x^2 - 5x + 6) = 0$.Factoring the quadratic: $(x + 2)(x

Vedclass · Accepted Answer

$2^{15}$

Vedclass · Answer

(A) Given $A = \{ x \in Z : 2^{(x + 2)(x^2 - 5x + 6)} = 1 \}$.Since $2^0 = 1$,we have $(x + 2)(x^2 - 5x + 6) = 0$.Factoring the quadratic: $(x + 2)(x - 2)(x - 3) = 0$.Thus,$x = -2, 2, 3$. So,$A = \{ -2, 2, 3 \}$ and $n(A) = 3$.Given $B = \{ x \in Z : -3 Adding $1$ to all parts: $-2 Dividing by $2$: $-1 Since $x \in Z$,$B = \{ 0, 1, 2, 3, 4 \}$ and $n(B) = 5$.The number of elements in $A 	imes B$ is $n(A) 	imes n(B) = 3 	imes 5 = 15$.The number of subsets of a set with $n$ elements is $2^n$.Therefore,the number of subsets of $A 	imes B$ is $2^{15}$.

Let $Z$ be the set of integers. If $A = \{ x \in Z : 2^{(x + 2)(x^2 - 5x + 6)} = 1 \}$ and $B = \{ x \in Z : -3 < 2x - 1 < 9 \}$,then the number of subsets of the set $A \times B$ is:

Similar Questions

Let $U = \{ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 \}$,$A = \{ 1, 2, 5 \}$,and $B = \{ 6, 7 \}$. Then $A \cap B'$ is:

Which of the following sets is non-empty?

If $U = \{a, b, c, d, e, f\}$ and $A = \{a, b, c\}$,find $(U \cup A^{\prime})$.

The domain of the function $f(x) = \ln(x - [x])$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module