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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 in Set Theory & Algebra by Veteran (56k points)   | 272 views

3 Answers

+13 votes
Best answer
Answer D

$(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 (10.2k points)  
selected by
+7 votes

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 (2.6k points)  
Yes absolutely correct , will get 1 , that is U
+1 vote

so option d 

answered by Active (1.1k points)  
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