Question

A die is thrown describe the following events:
(i) A : a number is less than $7$
(ii) B : a number is greater than $7$
(iii) C : a multiple of $3$
(iv) D : a number less than $4$
(v) E : an even number greater than $4$
(vi) F : a number not less than $3$
Also find $A\cup B,A\cap B,B\cup C,E\cap F,D\cap E,A-C,D-E,E\cap F^{\prime },F^{\prime }$

Answer 1

When a die is thrown , the possible outcomes are $1,2,3,4,5$ or $6$.
So, $U=S=\{1,2,,4,5,6\}$
(i) $A=\{1,2,3,4,5,6\}$
(ii)$B=\varphi$
(iii)$C=\{3,6\}$
(iv)$D=\{1,2,3\}$
(v)$E=\left\{6\right\}$
(vi)$F=\{4,5,6\}$
Now, $A\cup B=\{1,2,3,4,5,6\}$
$A\cap B=\varphi$
$B\cup C=\{3,6\}$
$E\cap F=\left\{6\right\}$
$D\cap E=\varphi$
$A-C=\{1,2,4,5\}$
$D-E=\{1,2,3\}$
$E\cap F^{\prime }=E-F=\varphi$
$F^{\prime }=U-F=\{1,2,3\}$