Complement

Q.

If in a class of $100$ students, $60$ like mathematics, $72$ like physics, $68$ like chemistry and no student likes all three subjects, then the number of students who didn't like mathematics and chemistry is ?

Q.

Write the following sets in set builder form (1/4, 2/5, 3/6, 4/7, 5/8)

Q.

A man has 7 relatives, 4 of them are ladies and 3 of them are gentleman, his wife has also 7 relatives 4 of them are gentleman and 3 of them are ladies.In how many ways can they invite a dinner party for 3 ladies and 3 gentlemen so that there are 3 of the man's relatives and 3 of the wife' relatives.

Q. Two finite sets have m and n elements respectively. The total number of subsets of first set is 56 more than the total number of subsets of the second set. The values of m and n respectively are.

1. 5, 1
2. 6, 3
3. 8, 7
4. 7, 6

Q.

For any set A , (A')' is equal to

1. $\varphi$

2. A'

3. A

4. none of these

Q.

Negation of the conditional, If it rains, I shall go to school is

1. It rains and I shall go to school

2. It rains and I shall not go to school

3. It does not rain and I shall go to school

4. None of the above

Q.

A subset B of the set of first 100 positive integers has the property that no two elements of B sum to 125. What is the maximum possible number of elements in B?

Q. Let $U=\{1,2,3,4,5,5,6,7,8,9,10\}$ and $A=\{1,3,5,7,9\}$. Find $A^{\prime }$.

Q.

If A = {1, 2, 3, 4} and B = {5, 6, 7, 8}, then which function is one-one and onto?

1. f₂ = {(1, 6), (2, 8), (3, 8), (4, 5)}

2. f₄ = {(1, 8), (2, 7), (3, 6), (4, 7)}

3. f₃ = {(1, 5), (2, 7), (3, 8), (4, 5)}

4. f₁= {(1, 5), (2, 7), (3, 8), (4, 6)}

Q. In a class of $100$ students, $60$ like mathematics, $72$ like physics, $68$ like chemistry and no student likes all three subjects. Then number of students who don't like mathematics and chemistry is

Q.

All $\_\_\_\_\_$ triangles are similar.

1. reflex

2. isosceles

3. right angled

4. equilateral

Q.

Q. Let $A$ and $B$ be sets. If $A\cap X=B\cap X=\varphi$ and $A\cup X=B\cup X$ for some set $X,$ show that $A=B$

Q.

1. $36$
2. $24$
3. $30$
4. none of these

Q.

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

(i) {3, 4}⊂ A

(ii) {3, 4}}∈ A

(iii) {{3, 4}}⊂ A

(iv) 1∈ A

(v) 1⊂ A

(vi) {1, 2, 5} ⊂ A

(vii) {1, 2, 5} ∈ A

(viii) {1, 2, 3} ⊂ A

(ix) Φ ∈ A

(x) Φ ⊂ A

(xi) {Φ} ⊂ A

Q. If A = {1, 2, 3, 4} B = {8}, then number of nonempty relations from A to B

Q. Prove that ${}^n{P}_n{=}^n{P}_{n-1}$

Q. If $3p+2q=r,$ where $p,q,r$ are prime numbers, then which of the following statements is (are) possible

1. $p$ can be an odd number
2. $p$ can be an even number
3. $q$ can be an odd number
4. $q$ can be an even number

Q.

Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that

(i) A × (B ∩ C) = (A × B) ∩ (A × C)

(ii) A × C is a subset of B × D

Q. State true or false:
$P\left(A\right)\cup P\left(B\right)=P(A\cup B)$

Q. In a survey, it was fond that $65$% of the people watched news on TV, $40$% read in newspaper, $25$% read newspaper and watched TV. What percentage of people neither watched TV nor read newspaper?

1. $0$%
2. $5$%
3. $20$%
4. $10$%

Q.

Let f be the subset of Z × Z defined by f= {(ab, a+b) : a, b belongs to Z } . Is f a function from Z to Z ?

Q.

Let f be the subset of Z × Z defined by f = {(ab, a + b): a, b ∈ Z}. Is f a function from Z to Z: justify your answer.

Q. Evaluate $\underset{x\to 0}{lim}{\left(\frac{a^x+b^x+c^x}{x}\right)}^{1/x};(a,b,c>0)$.

Q. The highest common factor of $48,92,132$ is

1. $2$
2. $3$
3. $4$
4. $6$

Q.

If U = {a, b, c, d, e, f, g, h}, find the complements of the following sets:

(i) A = {a, b, c}

(ii) B = {d, e, f, g}

(iii) C = {a, c, e, g}

(iv) D = {f, g, h, a}

Q. If $U=\{1,2,3,4,5,6\}$ and $A=\{2,3,4,5\}$ then find $A^{\prime }$.

Q. How will you identify the sequence is an infinite geometric progression?

1. An geometric sequence containing finite number of terms
2. An geometric sequence containing infinite number of terms
3. An arithmetic sequence containing finite number of terms
4. An arithmetic sequence containing infinite number of terms

Q. If $n\left(U\right)=48,n\left(A\right)=28,n\left(B\right)=33$ and $n(B–A)=12$, then $n(A\cap B{)}^C=$

Q. Let $A,B$ are mutually independent events then show that $\overline{A},B$ are also mutually independent events.