If A = {2x : x ϵ N}, 1 ≤ x < 4}, B = {x + 2) : x ϵ N and 2 ≤ x < 5} and C = {x : x ϵ N and 4 < x < 8}, find:
Question:
If $A=\{2 x: x \in N\}, 1 \leq x<4\}, B=\{x+2): x \in N$ and $2 \leq x<5\}$ and $C=\{x: x \in N$ and $4 (i) $\mathbf{A} \cap \mathbf{B}$ (ii) $\mathbf{A \cup B}$ (iii) $(\mathrm{A} \cup \mathrm{B}) \cap \mathrm{C}$
Solution:
Given; A = {2x : x ϵ N}, 1 ≤ x < 4}, B = {x + 2) : x ϵ N and 2 ≤ x < 5} and C = {x : x ϵ N and 4 < x < 8}
According to the given conditions; A = {2, 4, 6}, B = {4, 5, 6} and C = {5, 6, 7}
(i) $A \cap B=\{4,6\}$
(ii) $A \cup B=\{2,4,5,6\}$
(iii) $(A \cup B) \cap C=\{5,6\}$
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