Set Theory Test 32

Result

Set Theory Test 32

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Question 1
1 / -0

If A and B are any two sets, then $$A\bigcup (A\bigcap B)$$ is equal to

A
$$A$$

B
$$B$$

C
$$A'$$

D
$$B'$$

Solution
Question 2
1 / -0

Let U be set with number of elements in U is 2009.
Consider the following statements :
I if A, B are subsets of U with n $$(A \cup B)= 280 $$ then $$n(A'\cap B')=x_{1}^{3}+x_{2}^{3}=y_{1}^{3}+y_{2}^{3}$$ for some positive integers $$x_{1},x_{2},y_{1},y_{2},$$ II If A is a subset of U with n (A) = 1681 and out of these 1681 elements, exactly 1075 elements below to a subset B of U, then $$n(A-B)=m^{2}+P_{1}P_{2}P_{3}$$ for some positive integer m and distinct primes $$P_{1}P_{2}$$ Which of the statements given above is / are correct ?

A
I only

B
II only

C
Both I and II

D
Neither I nor II.

Solution
Question 3
1 / -0

Directions For Questions

If $$A = \{1, 2, 5, 7, 9, 10\}, B = \{3, 4\}$$ then

...view full instructions

The number of subjections from $$A$$ to $$B$$ is

A
$$62$$

B
$$30$$

C
$$10$$

D
$$64$$

Solution
Question 4
1 / -0

Given $$n(U) =20, n(A) =12, n(B) =9, n(A \cap B) =4$$, where U is the universal set, A and B are subset of U, then $$n((A \cup B)^C)=$$

A
$$17$$

B
$$9$$

C
$$11$$

D
$$3$$

Solution
Question 5
1 / -0

If n(A)=115, n(B)=326, n(A-B)=47, then $$n(A\cup B)$$ is equal to

A
373

B
165

C
370

D
none of these

Solution

$$n(A)=115$$
$$n(B)=326$$
$$n(A-B)=47$$
$$\therefore$$ $$n\left( A\cap B \right) =n\left( A \right) -n\left( A-B \right) $$
$$=115-47=68$$
$$\therefore$$ $$n\left( A\cup B \right) =n\left( A \right) +n\left( B \right) -n\left( A\cap B \right) $$
$$=115+326-68$$
$$=326+47$$
$$=373$$
Option A.
Question 6
1 / -0

X and Y are two sets and $$f:X\rightarrow Y$$. If $$f(c)=\left\{ y;c\subset X,y\subset Y \right\} $$ and $${ f }^{ 1 }(d)=\left\{ x;d\subset Y,x\subset X \right\} $$, then the true statement is

A
$$f({ f }^{ 1 }(b))=b$$

B
$$f({ f }^{ 1 }(a))=a$$

C
$$f({ f }^{ 1 }(b))=b,b\subset y$$

D
$$f({ f }^{ 1 }(a))=a,a\subset x$$
Question 7
1 / -0

Let N= {1, 2, 3, ........., 10}, then sum of the product of number taken two at a time from the set N is

A
$$55\times 24$$

B
$$45\times 24$$

C
$$512\times 45$$

D
$$55\times 12$$

Solution
Question 8
1 / -0

The set $$(A\cap B')'\cup (B\cap C)$$ is equal to?

A
$$A'\cup B\cup C$$

B
$$A'\cup B$$

C
$$A'\cup C'$$

D
$$A'\cap B$$

Solution

$$\left( A\cap B' \right) '\cup \left( B\cap C \right) $$
$$=\left( A\cap \bar B \right)\cup \left( B\cap C \right) $$
$$=\left( \bar A\cap B\right)\cup \left( B\cap C \right) $$
$$=\bar A\cup B\cup C$$
Hence, the answer is $$ A'\cup B\cup C.$$
Question 9
1 / -0

if S is a set of p(x) is polynomial of degree <2 such that p(0)=, P(1)=1, p(x)>0 $$\forall \quad x\quad \varepsilon $$ (0, 1) then

A
S=0

B
$$S=ax+91-1){ x }^{ 2 }\forall a\varepsilon (0,\infty )$$

C
$$S=ax+(1-a){ x }^{ 2 }\forall a\varepsilon R$$

D
$$S=ax+(1-a){ x }^{ 2 }\forall a\varepsilon R(0,\quad 2)$$

Solution
Question 10
1 / -0

The solution set of $$x^{2}+5x+6=0 $$ is ........

A
{2,3}

B
{-2,-3}

C
{2,-3}

D
{-2,3}

Solution