If P - Q - P - R - P - Q - X- Then how many values can X have-

P ∪ ( Q ∩ R ) = (P ∪Q) ∩(P ∪R) #160; #160;As union distributes over intersection.Hence, X=R. ...

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Standard IX

Mathematics

Distributive Property

If P ∪ Q ...

Question

If (P $\cup$ Q) $\cap$ (P $\cup$ R) = P $\cup$ (Q $\cap$ X). Then how many values can $X$ have?

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Solution

$P \cup$ ( $Q$ \capR $) =$ (P \cup Q) \cap (P \cup R)$
As union distributes over intersection.
Hence, $X = R .$

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If (P ∪ Q) ∩ (P ∪ R) = P ∪ (Q ∩ X). Then how many values can X have?

P∪ (Q\capR)= (P \cup Q) \cap (P \cup R)$ As union distributes over intersection.Hence, X=R.

If (P $\cup$ Q) $\cap$ (P $\cup$ R) = P $\cup$ (Q $\cap$ X). Then how many values can $X$ have?

$P \cup$ ( $Q$ \capR $) =$ (P \cup Q) \cap (P \cup R)$
As union distributes over intersection.
Hence, $X = R .$