348 views

If P, Q, R are subsets of the universal set U, then $$(P\cap Q\cap R) \cup (P^c \cap Q \cap R) \cup Q^c \cup R^c$$ is

1. $Q^c \cup R^c$
2. $P \cup Q^c \cup R^c$
3. $P^c \cup Q^c \cup R^c$
4. U
asked | 348 views

$(P∩Q∩R)\cup (P^c∩Q∩R)\cup Q^c\cup R^c \\=(P∪P^c)∩(Q∩R)∪Q^c∪R^c \\=(Q∩R)∪Q^c∪R^c \\=(Q∩R)∪(Q∩R)^C \\= U$
answered by Veteran (10.3k points)
selected

Can we treat these like Boolean expression and solve?

Like PQR + P'QR + Q' + R'. and minimise this.

Is this method always correct?
@Praveen Sir?
@Arjun Sir?

answered by Loyal (2.8k points)
Yes absolutely correct , will get 1 , that is U

so option d

answered by Active (1.3k points)

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+1 vote