If P - x-x -W-and-4-x -8 - and Q - x-x -N-and-x- -6 - Find - i P - Q and P - Q ii Is P - Q-P - Q

(i) P = (4, 5, 6, 7, 8) Q = (1, 2, 3, 4, 5) P ∪ Q = (1, 2, 3, 4, 5, 6, 7, 8) (P ∩ Q) = (4, 5) (ii) Yes, all the element of set P ∪ Q are contained in the set (P ...

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Byju's Answer

Standard VIII

Mathematics

Subset

If P = x:x ∈...

Question

If P = ${x : x \in W a n d 4 \leq x \leq 8}$ , and Q = ${x : x \in N a n d x < 6}$ . Find : (i) $P \cup Q$ and $P \cap Q$ (ii) Is $(P \cup Q) \supset (P \cap Q)$

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Solution

(i) P = (4, 5, 6, 7, 8) Q = (1, 2, 3, 4, 5) $P \cup Q$ = (1, 2, 3, 4, 5, 6, 7, 8) $(P \cap Q)$ = (4, 5)

(ii) Yes, all the element of set $P \cup Q$ are contained in the set $(P \cap Q)$ . Therefore $P \cup Q$ is a proper subset of $(P \cap Q)$ .

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If P = {x:x ∈ W and 4 ≤ x≤ 8}, and Q = {x:x ∈ N and x < 6}. Find : (i) P∪Q and P∩Q (ii) Is (P∪Q)⊃(P∩Q)

(i) P = (4, 5, 6, 7, 8) Q = (1, 2, 3, 4, 5) P∪Q = (1, 2, 3, 4, 5, 6, 7, 8) (P∩Q) = (4, 5) (ii) Yes, all the element of set P∪Q are contained in the set (P∩Q). Therefore P∪Q is a proper subset of (P∩Q).

If P = ${x : x \in W a n d 4 \leq x \leq 8}$ , and Q = ${x : x \in N a n d x < 6}$ . Find : (i) $P \cup Q$ and $P \cap Q$ (ii) Is $(P \cup Q) \supset (P \cap Q)$

(i) P = (4, 5, 6, 7, 8) Q = (1, 2, 3, 4, 5) $P \cup Q$ = (1, 2, 3, 4, 5, 6, 7, 8) $(P \cap Q)$ = (4, 5)

(ii) Yes, all the element of set $P \cup Q$ are contained in the set $(P \cap Q)$ . Therefore $P \cup Q$ is a proper subset of $(P \cap Q)$ .