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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
Let $\bar{P}$ and $\bar{Q}$ denote the complements of two sets P and Q. Then the set $(P-Q)\cup (Q-P) \cup (P \cap Q)$ is
Solution
Expression: \((P - Q) \cup (Q - P) \cup (P \cap Q)\)
Recall: \(P - Q = P \cap \bar{Q}\) and \(Q - P = Q \cap \bar{P}\).
Thus the union consists of three mutually exclusive parts:
- Elements only in \(P\): \(P \cap \bar{Q}\)
- Elements only in \(Q\): \(Q \cap \bar{P}\)
- Elements in both: \(P \cap Q\)
The union of these three pieces is precisely all elements that are in \(P\) or \(Q\):
\((P - Q) \cup (Q - P) \cup (P \cap Q) = P \cup Q\).
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