GATE CSE
First time here? Checkout the FAQ!
x
+5 votes
367 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 in Set Theory & Algebra by Veteran (58.2k points)   | 367 views

3 Answers

+15 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 (10.3k points)  
selected by
+8 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 (2.8k points)  
Yes absolutely correct , will get 1 , that is U
+4 votes

so option d 

answered by Active (1.3k points)  


Top Users Mar 2017
  1. rude

    4758 Points

  2. sh!va

    3014 Points

  3. Rahul Jain25

    2830 Points

  4. Kapil

    2636 Points

  5. Debashish Deka

    2450 Points

  6. 2018

    1514 Points

  7. Vignesh Sekar

    1422 Points

  8. Akriti sood

    1314 Points

  9. Bikram

    1286 Points

  10. Sanjay Sharma

    1076 Points

Monthly Topper: Rs. 500 gift card

21,484 questions
26,812 answers
61,056 comments
23,065 users