Number of Elements in a Cartesian Product

Q. Prove that if A has n element then its power set has 2n element!

Q. If 𝒙 + 𝟏 is one of the factors of $3x^3-3x$, then the other two factors are_____.

1. x - 1, 1 - x
2. x, x - 1
3. x + 1, 2x - 1
4. x, 1 - x

Q. if the number of subsets of set A exceeds the number of subsets of set B by 960. find the number of elements in set A and set B .

Q. If $A$ and $B$ are two sets containing four and two elements, respectively. Then, the number of subsets of the set $A\times B$ each having atleast three elements are

1. 219
2. 256
3. 275
4. 510

Q. State true or false.
$n(A\times B)=n(B\times A)=n\left(A\right)\times n\left(B\right)$​

1. False
2. True

Q.

If $A=\{1,2,3\}$ and $B=\{4,5\},$ then $A\times B=$ ___.

1. $\left\{\right(1,4),(1,5),(2,4),(2,5),(3,4),(3,5\left)\right\}$

2. $\left\{\right(4,1),(4,2),(4,3),(5,1),(5,2),(5,3\left)\right\}$

3. $\left\{\right(1,2),(1,3),(2,3),(4,5\left)\right\}$

4. $\left\{\right(1,4),(1,5),(2,4),(2,5\left)\right\}$

Q.

If set A = {1, 2, 3} and set B = {2, 3, 5, 7}. Then the number of elements in A $\times$ B is ___

Q. If $A=\{x:x=6n,n\in W$ and $n<6\},$ $B=\{x:x=2n,n\in N$ and $2<n\le 9\}$ and $C=\{x:x=3n,n\in N$ and $4\le n<10\}$, then show that $A-(B\cap C)=(A-B)\cup (A-C)$

Q.

If set A = {1, 2, 3} and set B = {2, 3, 5, 7}. Then the number of elements in A $\times$ B is ___

Q. If U = {1, 2, 3, 4, 5} and A = {2, 5, 1}. The number of elements in a set A' is ___.

1. 5
2. 3
3. 2
4. 4

Q. How do you convert $52$ cups into quarts ?

Q. A street vendor sells two types of newspapers, one for $\$0.25$ and the other for $\$0.40$. The total amount collected for $100$ newspaper is $\$28.00$. How many newspapers did street vendor sell at $\$0.25$?

1. $80$
2. $70$
3. $60$
4. $100$

Q. { $a,d,g,h$ } are the elements of $\xi -B$ or $B^{{}^{\prime }}$.