Let A={1,2,{3,4},5}.Which of the following statements are incorrect and why?
{3,4}\(\subset\)A

3

(a)

If n(A) = 4, n(B) = 5, n(U) = 7 and n(A\(\cap \)B) = 2, then find the value of n(A\(\cup \)B)'

3

(a)

In a class of 60 students, 25 students play cricket, 20 students play Tennis and 10 students play both the gmes. Then, find the number of students who play neither games.

3

(a)

Describe the following set in Roster form. {X: X is positive integer and a divisor of 9}

3

(a)

Find the symmetric difference of sets A={1,3,5,6,7} and B ={3,7,8,9}

3

(a)

Draw the Venn diagram of the following:
A' \(\cap\) (B \(\cup\) C)

3

(a)

Draw the Venn diagram of the following:
A' \(\cap\) (C - B)

3

(a)

If S and T are two sets such that S has 21 elements T has 32 elements and S \(\cap\) T has 11 elements, how many elements does S \(\cup\) T have?

3

(a)

In a group of 800 people, 550 can speak Hindi and 450 can speak English. How many can speak both Hindi and English?

3

(a)

A college awarded 38 medals in football, 15 in basketball and 20 in cricket. If these medals went to a total of 58 men and only three men got medals in all the three sports, how many received medals in exactly two of the three sports?
[ Hint: Here n(F) = 38, n(B) = 15, n(C) = 20, n(F \(\cup\) B \(\cup\) C) = 58 and n(F \(\cap\) B \(\cap\) C) = 3.
We know that n(F\(\cup\) B \(\cup\) C) =n(F) +n(B) +n(C)-n(F\(\cap\)B)-n(B nC)-n(F\(\cap\) C) +n(F\(\cap\)B \(\cap\)C).
\(\therefore\) n(F \(\cap\) B) + n(B \(\cap\) C) + n(F \(\cap\) C) = 18
\(\therefore\) Number of men who received medals in exactly two of three sports
= n(F \(\cap\) B) + n(B \(\cap\) C) + n(F \(\cap\) C) - 3 n(F \(\cap\) B \(\cap\) C) = 18 - 3 x 3 = 9.]

3

(a)

If A and B be two sets having 4 and 8 distinct elements respectively, find the minimum and maximum number of elements in A \(\cup\) B
[ Hint: For minimum n(A \(\cap\) B) = 0 and for maximum n(A \(\cap\) B) = 4]

3

(a)

Decide among the following sets, which sets are subsets of one and another:
A = {x : x ∈ R and x satisfies x² - 8x + 12 =0}
B = {2,4, 6}, C = {2, 4, 6, 8,............}, D = {6}

3

(a)

Let A, B and C be three sets, then prove that: A - (B \(\cup\) C) = (A - B) \(\cap\) (A - C)

3

(a)

Let A, Band C be three sets, then prove that:
A - (B - C) = (A - B) \(\cup\) (A \(\cap\) C)

3

(a)

Let \(T=[x:\frac{x+5}{x-7}-5=\frac{4x-40}{13x-x}]\) Is T an empty set? Justify your answer.

3

(a)