Universal Set

Q. What universal set (s) would you propose for each of the following: (i) The set of right triangles (ii) The set of isosceles triangles

Q.

The minimum number of elements that must be added to the relation R = {(1, 2), (2, 3)} on the subset of natural numbers so that is an equivalence is

1. 4

2. 7

3. 6

4. 5

Q.

Let A and B be two non empty sets such that $n\left(A\right)=5,n\left(B\right)=6$ and $n(A\cap B)=3$.

Find (i) $n(A\times B)$,

(ii) $n(B\times A)$ and

(iii) $n(A\times B)\cap (B\times A)$

Q. A relation from P to Q is

1. A universal set of $P\times Q$
2. $P\times Q$
3. An equivalent set of $P\times Q$
4. A subset of $P\times Q$

Q.

Given the set A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}, which of the following may be considered as universal set (s) for all the three sets A, B, and C?

(i) {0, 1, 2, 3, 4, 5, 6}

(ii) $\Phi$

(iii) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

(iv) {1, 2, 3, 4, 5, 6, 7, 8}

Q. Find the number of numbers between 1 and 10^{10} which contains the digit 1.

Q. The ordered pairs (2, 7), (4, 8)and (5, 9) are among 9 elements of the set A× B.Determine the other elements of A×

Q.

Which of the following sets are finite or infinite?

(i) The set of months of a year

(ii) {1, 2, 3, ....................}

(iii) {1, 2, 3, .................... 99, 100}

(iv) The set of positive integers greater than 100.

(v) The set of prime numbers less than 99.

Q. The negation of ‘Paris is in France and London is in England’ is ___.

1. Paris is in England and London is in France
2. Paris is not in France or London is not in England
3. Paris is in England or London is in France
4. Paris is not in France and London is not in England

Q.

If $A$ = $\{x:x^2-3x+2=0\}$, and R is a universal relation on A, then R is

1. 

2. 

3. 

4. 

Q. Find the polar form of the complex number -5.

Q.

From the following Venn diagram, A' is

1. {2, 4, 6, 8, 9, 10}

2. {1, 3, 5, 7, 9}

3. {1, 3, 5, 7}

4. {2, 4, 6, 8, 10}

Q.

If A={$x:xϵM$, x is a factor of 6}$=\{1,2,3,6\}$
and B={$x:xϵN$, x is a factor of 8} = $\{1,2,4,8\}$. Then find:

$\left(i\right)A\cup B$

$\left(ii\right)A\cap B$

$\left(iii\right)A-B$

$\left(iv\right)B-A$

Q. 24. If A= {1, 2, 3, 4, 5, 6} then the number of subsets of A which contains atleaSt 3 elements a) 6P2 b) 6P3 c) 6C2 d) 6C3

Q.

The statement $p\Rightarrow \sim q$ is equivalent to

1. $q\Rightarrow p$

2. $\sim q\Rightarrow p$

3. $\sim q\vee \sim p$

4. $\sim p\vee q$

Q. 35. How many triangles and straight line can be formed by joining any of the 12 points in a plane of which 4 are collinear?

Q. Let U be the universal set containing 700 elements. If A, B are sub-sets of U such that $n\left(A\right)=200,n\left(B\right)=300\mathrm{and}\left(A\cap B\right)=100$. Then $n\left(A\text{'}\cap B\text{'}\right)=$
(a) 400
(b) 600
(c) 300
(d) none of these.

Q.

Write each of the following intervals in the set-builder from:
(i) A=(2, 5)

(ii) B=[-4, 7]

(iii) C=[-8, 0)

(iv) D= (5, 9]

Q. Given the sets A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}, which of the following may be considered as universals set (s) for all the three sets A, B and C (i) {0, 1, 2, 3, 4, 5, 6} (ii) Φ (iii) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} (iv) {1, 2, 3, 4, 5, 6, 7, 8}

Q. Let f(x) be an odd function in the interval [-T/2, T/2] with a period T, then φ(x) = integration (lower limit =a, upper limit =x) f(t) dt is A) periodic with period T B) periodic with period 2T C)periodic with period aT D) non periodic

Q. The set of numbers which are the multiples of 5 is: (a) a finite set (b)an infinite set(c)a singleton set (d) none of these.

Q. For any two sets of A and B, prove that:
(i) $A\text{'}\cup B=U\Rightarrow A\subset B$
(ii) $B\text{'}\subset A\text{'}\Rightarrow A\subset B$

Q. Universal set for the set of right triangles

Q.

State whether each of the following statement are true or false. If the statement is false, rewrite the given statement correctly.

(i) If P = {m, n} and Q = {n, m}, then P × Q = {(m, n), (n, m)}.

(ii) If A and B are non-empty sets, then A × B is a non-empty set of ordered pairs (x, y) such that x ∈ A and y ∈ B.

(iii) If A = {1, 2}, B = {3, 4}, then A × (B ∩ Φ) = Φ.

Q. where are the imaginary numbers used?

Q. For any two sets A and B, prove that : $A\text{'}-B\text{'}=B-A$

Q.

Assume that P (A) = P (B). Show that A = B.

Q. If $A=\{1,3,5\},B=\{2,4,6\},C=\{1,4\}$ then which of the following is universal set?

1. $\{0,1,2,3,4,5\}$
2. $\{1,2,3,4,6\}$
3. $\{1,2,3,4,5,6,7,8\}$
4. $\varphi$

Q.

Let U be the set of all triangles in a plane. If A is the set of all triangles with at least one angle different from 60°, what is?

Q. For any two sets A and B,
(a) A
(b) B
(c) ϕ
(d) none of these.