Consider the following for any three non empty sets A, B and C1 A−(B∪C)=(A−B)∪(A−c)2 A−B=A−(A∩B)3 A=(A∩B)∪(A−B)which of the above is/are correct?

1. A(B∪C)=(A−B)∪(A−C)(A−B)∪(A−C)⇒ for all xεA and x ∈/ B ) or x ϵ A and x ∈/ B and X ∈/ C)⇒xϵA−(B∩C)Hence not correct 2.xε(A∩B(A∩B))⇒XϵAandx∈/A∩B\displaystyle \Rightarrow X\varepsilon (A\ and \ x \notin B)⇒Xε(A−B)3. xε[(A∩B)∪(A−B)]⇒(XεAandx∈/B)or(xϵB′)⇒xϵAandxεB∩B′⇒xεAandxεϕ⇒xϵA∪ϕ⇒xεAHence (1) is incorrect,

Get 2 FREE Instant-Explanations on Filo with code FILOAPP

Home

Consider the following for any three non empty sets A, B and C

Question

Consider the following for any three non empty sets A, B and C
1 $A - (B \cup C) = (A - B) \cup (A - c)$
2 $A - B = A - (A \cap B)$
3 $A = (A \cap B) \cup (A - B)$
which of the above is/are correct?

Only 1

2 and 3

1 and 2

1 and 3

Views: 723 students

Found 8 tutors discussing this question

Henry Discussed

Consider the following for any three non empty sets A, B and C
1

A - (B \cup C) = (A - B) \cup (A - c)

A - B = A - (A \cap B)

A = (A \cap B) \cup (A - B)

which of the above is/are correct?

13 mins ago

Discuss this question LIVE

13 mins ago

Text solutionVerified

A (B \cup C) = (A - B) \cup (A - C)

(A - B) \cup (A - C)

\Rightarrow

for all

x ε A

and x

\in /

B ) or x

ϵ

A and x

\in /

B and X

\in /

\Rightarrow x ϵ A - (B \cap C)

Hence not correct

x ε (A \cap B (A \cap B)) \Rightarrow X ϵ A an d x \in / A \cap B

\displaystyle \Rightarrow X\varepsilon (A\ and \ x \notin B)

\Rightarrow Xε (A - B)

x ε [(A \cap B) \cup (A - B)]

\Rightarrow (Xε A an d x \in / B) or (x ϵ B^{'})

\Rightarrow x ϵ A an d x εB \cap B^{'}

\Rightarrow x ε A an d x εϕ

\Rightarrow x ϵ A \cup ϕ \Rightarrow x ε A

Hence (1) is incorrect,

Was this solution helpful?

150

Report

One destination for complete JEE/NEET preparation

One destination to cover all your homework and assignment needs

Learn Practice Revision Succeed

Instant 1:1 help, 24x7

60, 000+ Expert tutors

Textbook solutions

Big idea maths, McGraw-Hill Education etc

Essay review

Get expert feedback on your essay

Schedule classes

High dosage tutoring from Dedicated 3 experts

Trusted by 4 million+ students

Stuck on the question or explanation?

Connect with our maths tutors online and get step by step solution of this question.

231 students are taking LIVE classes

Question Text	Consider the following for any three non empty sets A, B and C 1 $A - (B \cup C) = (A - B) \cup (A - c)$ 2 $A - B = A - (A \cap B)$ 3 $A = (A \cap B) \cup (A - B)$ which of the above is/are correct?
Answer Type	Text solution:1
Upvotes	150

Consider the following for any three non empty sets A, B and C1 A−(B∪C)=(A−B)∪(A−c)2 A−B=A−(A∩B)3 A=(A∩B)∪(A−B)which of the above is/are correct?

Text solutionVerified

Practice questions from similar books

Consider the following for any three non empty sets A, B and C
1 $A - (B \cup C) = (A - B) \cup (A - c)$
2 $A - B = A - (A \cap B)$
3 $A = (A \cap B) \cup (A - B)$
which of the above is/are correct?