Question

Find the complement of C given that : U=Z and C= { x | x less than or equal to -5, x is an element of Z}

Answer 1

$\underline{\pmb{Given\: -}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \rm{U = Z}$

Where,

• U is a universal set
• Z is a set of all Integers

$\rm{C = \{x : x \leqslant - 5 \: and \: x \in \: Z \}}$

$\underline{\pmb{Find\:-}}$

• Value of C
• Complement of C

$\underline{\pmb{Solution \: -}}$

$\rm{C = \{x : x \leqslant - 5 \: and \: x \in \: Z \}} \\ \boxed{\rm{C = \{ \: - 5 , - 4 , - 3,- 2,- 1 , - \infty \}}}$

Complement of C '

$\: \rightarrow\bf{C' = U - C} \\ \: \: \: \: \ \rm{C' = \{Z - ( -5 , - 4, - \infty ) } \} \\ \: \: \boxed{\rm{ \underline{C ' = \{ - 4, - 3, - 2 ,- 1,0 ,1 ,2 ,\infty \}}}}$

#Gunjan