June 2024 – Page 16 – chillimath.com

4. Show that the following four conditions are equivalent:(i) A⊂B (ii) A–B=(phi) (iii) A∪B=B (iv) A∩B=A SetsMiscellaneous Exercise Previous Next Class 11SetsMiscellaneous Exercise1. Decide, among the following sets, which sets are subsets of one and another:A={x : x∈R and x satisfy x2–8x+12=0}, B={2,4,6}, C={2,4,6,8, . . . }, D={6}.2. In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.(i) If x∈A and A∈B, then x∈B(ii) If A⊂B and B∈C, then A∈C(iii) If A⊂B and B⊂C, then A⊂C(iv) If A⊄B and B⊄C, then A⊄C(v) If x∈A and A⊄B, then x∈B(vi) If A⊂B and x∉B, then x∉A3. Let A, B, and C be the sets such that A∪B=A∪C and A∩B=A∩C. Show that B=C.4. Show that the following four conditions are equivalent:(i) A⊂B (ii) A–B=(phi) (iii) A∪B=B (iv) A∩B=A5. Show that if AB, then C–B ⊂ C–A.6. Show that for any sets A and B,A=(A∩B)∪(A–B) and A∪(B–A)=(A∪B).7. Using properties of sets, show that(i) A∪(A∩B)=A (ii) A∩(A∪B)=A.8. Show that A∩B=A∩C need not imply B=C.9. Let A and B be sets. If A∩X=B∩X=(phi) and A∪X=B∪X for some set X, show that A=B.(Hints A=A∩(A∪X), B=B∩(B∪X) and use Distributive law)10. Find sets A, B and C such that A∩B, B∩C and A∩C are non-empty sets and A∩B∩C=(phi). Leave A Comment Cancel Reply Logged in as chillimath. Log out » Comments Name Email Sign me up for the newsletter!

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Month: June 2024

Ncert Solutions Class 11 Chapter 1 Sets Miscellaneous Exercise Question 4

Ncert Solutions Class 11 Chapter 1 Sets Miscellaneous Exercise Question 3

Ncert Solutions Class 11 Chapter 1 Sets Miscellaneous Exercise Question 2

Ncert Solutions Class 11 Chapter 1 Sets Miscellaneous Exercise Question 1

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