Question

State which of the following sets are disjoint
(i) $A=\{2,4,6,8\};B=$ $\{$ $x:x$ is an even number $<10,x\in N\}$
(ii) $X=\{1,3,5,7,9\},Y=\{0,2,4,6,8,10\}$
(iii) $P=$ $\{$ $x:x$ is a prime $<15$$\}$
$Q=$$\{$ $x:x$ is a multiple of 2 and $x<16$$\}$
(iv) $R=\{a,b,c,d,e\},S=\{d,e,a,b,c\}$

Answer 1

If two sets A and B are said to be disjoint if$A\cap B=\varphi$.

$\left(1\right)A=\{2,4,6,8\}$

$B=\{2,4,6,8\}$

$A=B$

So, $A$ and $B$ are not disjoint.

$\left(2\right)X=\{1,3,5,7,9\}$

$Y=\{0,2,4,6,8,10\}$

$X\cap Y=\varphi$

So, $X$ and $Y$ are disjoint.

$\left(3\right)P=\{2,3,5,7,11,13\}$

$Q=\{.........-4,-2,0,2,4,6,8,10,12,14\}$

$P\cap Q=\left\{2\right\}$

So, $P$ and $Q$ are not disjoint.

$\left(4\right)R=\{a,b,c,d,e\}$

$S=\{d,e,a,b,c\}$

$R\cap S=\{a,b,c,d,e\}$

So, $R$ and $S$ are not disjoint.