Q. 9 D5.0( 1 Vote )

# Using Venn diagram, verify whether the following are true:

A \ (B ∪ C) = (A \ B) ∩ (A \ C)

Answer :

A \ (B ⋃ C) = (A \ B) ⋂ (A \ C)

LHS:

Consider B ⋃ C,

Then, A \ (B ⋃ C)

= LHS

RHS:

Consider A \ B,

Then, consider A \ C,

Then, (A \ B) ⋂ (A \ C)

= RHS

∴ LHS = RHS

Hence proved.

Rate this question :

Let A **=** {10, 15, 20, 25, 30, 35, 40, 45, 50}**,** B **=** {1, 5, 10, 15, 20, 30} and C **=** {7, 8, 15, 20, 35, 45, 48}**.** Verify A \ (B ⋂ C) = (A \ B) ⋃ (A \ C).

If A and B are two sets and U is the universal set such that n(∪) = 700, n(A) = 200, n(B) = 300 and n (A ∩ B) = 100,find n(A’ ∩ B’).

Tamil Nadu Board - MathDraw Venn diagram of three sets A,B and C illustrating the following:

(i) A ∩ B ∩ C

(ii) A and B are disjoint but both are subsets of C

(iii) A ∩ (B\C)

(iv) (B ∪ C)\A

(v) A∪(B ∪ C)

(vi) C ∪ (B\A)

(vii) C ∩ (B ∪ A)

Tamil Nadu Board - MathWrite a description of each shaded area. Use symbols U, A, B, C,â,∩, ’ and \ as necessary

(i)

(ii)

(iii)

(iv)

Tamil Nadu Board - MathGiven that U = {a, b, c, d, e, f, g, h}, A = {a, b, f, g}, and B = {a, b, c}, verify De Morgan’s laws of complementation.

Tamil Nadu Board - MathLet U = {4, 8, 12, 16, 20, 24, 28}, A = {8, 16, 24} and B = {4, 16, 20, 28}. Find (A ∪ B)’ and (A ∩ B)’

Tamil Nadu Board - MathUse Venn diagram to verify (A ∩ B) ∪ (A\B) = A.

Tamil Nadu Board - MathUsing Venn diagram, verify whether the following are true:

(A ∪ B)’ = A’ ∩ B’

Tamil Nadu Board - MathUsing Venn diagram, verify whether the following are true:

A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

Tamil Nadu Board - MathUsing Venn diagram, verify whether the following are true:

A \ (B ∪ C) = (A \ B) ∩ (A \ C)

Tamil Nadu Board - Math