Question

Let U = {x|x = 2ⁿ, n $\in$ W, n > 8} be the universal set.
A = {y|y = 4ⁿ, n $\in$ W, n < 4} B = {z | z = 8ⁿ, b $\in$ W, n $\le$ 2}
then find (i) A' (ii) B' (iii) (A $\cup$ B)' (iv) (A $\cap$ B)' (v) (A $-$ B)'

Answer 1

U = {2⁰, 2¹, 2², 2³, 2⁴, 2⁵, 2⁶, 2⁷} = {1, 2, 4, 8, 16, 32, 64, 128}
A = {4⁰,4¹,4²,4³} = {1, 4, 16, 64}
B = {8⁰, 8¹, 8²} = {1, 8, 64}

(i) A' = {2, 8, 32, 128}

(ii) B' = {2, 4, 16, 32, 128}

(iii) $\left(\mathrm{A}\cup \mathrm{B}\right)$ = {1, 4, 8, 16, 64} and $\left(\mathrm{A}\cup \mathrm{B}\right)\text{'}$ = {2, 32, 128}

(iv) $\left(\mathrm{A}\cap \mathrm{B}\right)$ = {1, 64} and $\left(\mathrm{A}\cap \mathrm{B}\right)$^' = {2, 4, 8, 16, 32, 128}

(v) (A $-$ B) = { 4, 64} and (A $-$ B)' = {1, 2, 8, 16, 32, 128}