Home
Class 11
MATHS
(i) (AuuB)^(c) =…………… (ii) (AcapB)^(c)...

(i) `(AuuB)^(c)` =……………
(ii) `(AcapB)^(c)` = …………….

Text Solution

AI Generated Solution

The correct Answer is:
To solve the given question, we will use De Morgan's laws, which state: 1. \( (A \cup B)^c = A^c \cap B^c \) 2. \( (A \cap B)^c = A^c \cup B^c \) Now, let's solve each part step by step. ### (i) Find \( (A \cup B)^c \) **Step 1:** Identify the expression \( A \cup B \). - The union of sets \( A \) and \( B \) includes all elements that are in \( A \), in \( B \), or in both. **Hint:** Remember that the union combines all elements from both sets. **Step 2:** Apply the complement. - The complement of \( A \cup B \) includes all elements that are not in \( A \cup B \). **Hint:** The complement refers to everything outside the specified set. **Step 3:** Use De Morgan's law. - According to De Morgan's law, \( (A \cup B)^c = A^c \cap B^c \). **Final Answer for (i):** \[ (A \cup B)^c = A^c \cap B^c \] --- ### (ii) Find \( (A \cap B)^c \) **Step 1:** Identify the expression \( A \cap B \). - The intersection of sets \( A \) and \( B \) includes all elements that are in both \( A \) and \( B \). **Hint:** The intersection focuses on elements common to both sets. **Step 2:** Apply the complement. - The complement of \( A \cap B \) includes all elements that are not in both \( A \) and \( B \). **Hint:** Again, think of the complement as everything outside the specified set. **Step 3:** Use De Morgan's law. - According to De Morgan's law, \( (A \cap B)^c = A^c \cup B^c \). **Final Answer for (ii):** \[ (A \cap B)^c = A^c \cup B^c \] --- ### Summary of Answers: (i) \( (A \cup B)^c = A^c \cap B^c \) (ii) \( (A \cap B)^c = A^c \cup B^c \)
Promotional Banner

Topper's Solved these Questions

  • SETS

    MODERN PUBLICATION|Exercise OBJECTIVE TYPE QUESTIONS (C ) TRUE / FALSE QUESTINS|5 Videos

  • SETS

    MODERN PUBLICATION|Exercise OBJECTIVE TYPE QUESTIONS (D) VERY SHORT ANSWER TYPE QUESTION|17 Videos

  • SETS

    MODERN PUBLICATION|Exercise OBJECTIVE TYPE QUESTIONS (A )(MULTIPLE CHOICE QUESTIONS)|30 Videos

  • SEQUENCES AND SERIES

    MODERN PUBLICATION|Exercise CHAPTER TEST|12 Videos

  • STATISTICS

    MODERN PUBLICATION|Exercise Chapter Test|7 Videos

Similar Questions

Explore conceptually related problems

(a) If U= {1,2,3,……, 10} ,A = { 1,2,3,4,5}, B= {1,3,5,7,9} , C {2,4,8,10}, verify that : (i) (AuuB)^(c)=A^(c)capB^(c) (ii) (AcapB)^(c)=A^(c)uuB^(c) (iii) A-B=AcapB^(c) (iv) Acap(BuuC)=(AcapB)uu(AcapC) . (b) If U={1,2,3,4,5,6,7,8,9}, A={2,4,6,8} and B= {2,3,5,7}. Veify that : (i) (AuuB)^(c)=A^(c)capB^(c) (ii) (AcapB)^(c)=A^(c)uuB^(c) .

Let U={1,2,3,4,5,6,7,8,9},A = {2,4,6,8} and B={2,3,5,7} . Verify that : (i) (AuuB)^(c)=A^(c)capB^(c) (ii) (AcapB)^(c)=A^(c)uuB^(c) .

If U = {1,2,3,4,5,6},A = {1,2} , B = {3,4,5} , then : (i) A^(c)capB^(c) =……….. (ii) AuuB =…………. .

Prove that : (i) A^(c) - B^(c)=B-A (ii) B^(c)-A^(c)=A-B .

(i) ""^(50)C_(47)= ………. (ii) ""^(15)C_(14)= ………….

Prove that : (a) (i) Asub(AuuB) (ii) Bsub(AuuB) (b) (i) (AcapB)subA (ii) (AcapB)subB .

Prove that : (i) (AuuBuuC)^(c)=A^(c)capB^(c)capC^(c) (ii) (AcapBcapC)^(c)=A^(c)uuB^(c)uuC^(c) (iii) (AuuB)=(A-B)uu(B-A)uu(AcapB) .

(a) LetA= {1,2,3,4} ,B = {4,6,7,8,9} and C= {2,3,4,6,8} . Verify the following indentities : (i) (AuuB)uuC=Auu(BuuC) (ii) (AcapB)capC=Acap(BcapC)

If A , B and C are three non - empty finite sets such that n (A) =19 , n (B) = 15 , n (C ) =17, n(capB)=11,n(BcapC)=6,n(CcapA)=7andn(AcapBcapC)=5 . Also n (U) =50. (i) n(AcapB^(c)capC^(c)) (ii) n(BcapC^(c)capA^(c)) (iii) n(CcapA^(c)capB^(c)) (iv) n(CcapBcapC^(c)) (v) n(BcapCcapA^(c)) (vi) n(CcapAcapB^(c)) (vii) n(AuuBuuC) (viii) n((AuuBuuC)^(c)) .