Types of Sets

Is the following pairs of sets equal? Justify your answer.

$A=\left\{n:n\in Z\right.$ and $\left.n^2\le 4\right\}$ and $B=\left\{x:x\in R\right.$ and $\left.x^2-3x+2=0\right\}$.

State if the following set is a finite or an infinite set.

{$x:x\in N$ and $x$ is odd}

State if the following set is a finite or an infinite set.

{$x:x\in N$ and $x$ is prime}

State if the following set is a finite or an infinite set.

{$x:x\in N$ and $2x-1=0$}

State if the following set is a finite or an infinite set.

{$x:x\in N$ and $x^2=4$}

Is the interval of real numbers $[1,4)$ a finite set or infinite set$?$

Show that the set of letters needed to spell "CATARACT" and the set of letters needed to spell "TRACT" are equal.

Is the following pair of sets equal? Justify your answer.

$X$, the set of letters in $"\mathrm{ALLOY}"$ and $B$, the set of letters in $"\mathrm{LOYAL}"$.

Find the pairs of equal sets, if any. Give reasons:

$A=\left\{0\right\}$, 

$B=\{x:x>15$ and $x<5\}$,

$C=\left\{x:x-5=0\right\}$

$D=\left\{x:x^2=25\right\}$

$E=\{x:x$ is an integral positive root of the equation $x^2-2x-15=0\}$.

State if the following set is a finite or an infinite set.

{$x:x\in N$ and $\left(x-1\right)\left(x-2\right)=0$}

Two finite sets respectively have $x$ and $y$ number of elements. The total number of sub sets of the first is $56$ more than the total no. of sub sets of the second. The value of $x, y$ are respectively __________

The set of cubes of natural numbers is

What is mean by emptyset?

The set of integers between $-5 \mathrm{and} 5$.

The set $A=\left\{x:x\in R, x^2=16 \& 2x=6\right\}$ equals

As per question No.$\left(21\right)$ with same order of options (a) (b) (c) and (d) list the losing conditions.

As per question No.$\left(21\right)$ with same order of options (a) (b) (c) and (d) list the blocking conditions.

If four members $a,b,c,d$ of a decision making body are in a meeting to pass a resolution where rule of majority prevails list the wining coalitions. Given that $a,b,c,d$ own $50\%$, $20\%,15\%,15\%$ shares each.

If $A=\{0,1\}$ state which of the following statements are true:- (i) $\left\{1\right\}\subset \mathrm{A}$ (ii) $\left\{1\right\}\in \mathrm{A}$ (iii) $\varphi \in A$ (iv) $0\in A$ (v) $1\subset A$ (vi) $\left\{0\right\}\in A$ (vii) $\varphi \subset A$

with the same order of options (a), (b), (c) and (d) find the number having only coffee.