From the given Venn diagram, determine the following sets.

(i) $A\cup B$

(ii) $A\cap B$

(iii) $A-B$

(iv) $\left(A\cap B\right)\text{'}$

(i) {$x:x\in N$ and $\left(x-3\right)\left(x-4\right)=0$}

(ii) {$x:x\in N$ and $x$ is a prime number}

(iii) {$x:x\in N$ and $x^2<0$}

(iv) {$x:x\in N$ and $3x^2-27=0$}

The universal set $U=$ {$x:x$ is a letter in 'AN EXCELLENT BOOK'}

$P=$ {$x:x$ is a letter in word 'TALENT'}

$Q=$ {$x:x$ is a letter in the word 'BANANA'}
Draw the Venn diagram and find the following:

(i) $P\cup Q$

(ii) ${\left(P\cap Q\right)}^{\text{'}}$

(i) $n\left(B\right)$,

(ii) $n\left(B-A\right)$

(i) $A\cap \left(B\cup C\right)$

(ii) ${\left[\left(A\cup B\right)\cap C\right]}^{\text{'}}$

$A=${$x:x$ is a prime number}

$B=${$x: x$ is an even number}

Then verify, the following

(i) ${\left(A\cap B\right)}^{\text{'}}=A^{\text{'}}\cup B^{\text{'}}$

(ii) $A^{\text{'}}-B^{\text{'}}=B-A$

(i) $A-B$

(ii) $B^{\text{'}}$

(iii) $A^{\text{'}}$