Question

Choose the correct alternative answer for each of the following questions.

(i) If M = {1, 3, 5}, N = {2, 4, 6}, then M$\cap$N = ?

(A) {1, 2, 3, 4, 5, 6} (B) {1, 3, 5} (C) $\varphi$ (D) {2, 4, 6}

(ii) P = { x | x is an odd natural number, 1 < x $\le$5} How to write this set in roster form?

(A) {1, 3, 5} (B) {1, 2, 3, 4, 5} (C) {1, 3} (D) {3, 5}

(iii) P = {1, 2, ........., 10}, What type of set P is ?

(A) Null set (B) Infinite set (C) Finite set (D) None of these

(iv) M$\cup$N = {1, 2, 3, 4, 5, 6} and M = {1, 2, 4} then which of the following represent set N ?

(A) {1, 2, 3} (B) {3, 4, 5, 6} (C) {2, 5, 6}

(D) {4, 5, 6}

(v) If P$\subseteq$ M, then Which of the following set represent P $\cap$ (P $\cup$ M) ?

(A) P (B) M (C) P$\cup$M (D) P' $\cap$ M

(vi) Which of the following sets are empty sets ?

(A) set of intersecting points of parallel lines
(B) set of even prime numbers.

(C) Month of an english calendar having less than 30 days.

(D) P = { x | x $\in$ I, $-$1 < x < 1}

Answer 1

(i) We have,

M = {1, 3, 5}, N = {2, 4, 6}

M$\cap$N = $\varphi$ = Empty set

So, the correct option is (C).

(ii) Since, P = {x | x is an odd natural number, 1 < x $\le$5} = {3, 5}

So, the correct option is (D).

(iii) Since, the elements of set P = {1, 2, ..., 10} is finite.

So, set P is a finite set.

Hence, the correct option is (C).

(iv) We have, M $\cup$ N = {1, 2, 3, 4, 5, 6} and M = {1, 2, 4}

Since, {1, 2, 3} $\cup$ {1, 2, 4} = {1, 2, 3, 4} $\ne$ M $\cup$ N = {1, 2, 3, 4, 5, 6};

{3, 4, 5, 6} $\cup$ {1, 2, 4} = {1, 2, 3, 4, 5, 6} = M $\cup$ N = {1, 2, 3, 4, 5, 6};

{2, 5, 6} $\cup$ {1, 2, 4} = {1, 2, 4, 5, 6} $\ne$ M $\cup$ N = {1, 2, 3, 4, 5, 6}; and

{4, 5, 6} $\cup$ {1, 2, 4} = {1, 2, 4, 5, 6} $\ne$ M $\cup$ N = {1, 2, 3, 4, 5, 6}

So, the correct option is (B).

(v) We have, P$\subseteq$ M,

Now, P $\cap$ (P $\cup$ M) = P $\cap$ M = M (Since, P $\cup$ M = M; P$\subseteq$ M)

So, the correct option is (B).

(vi) Since,

the set of intersecting points of parallel lines = {};

the set of even prime numbers= {2};

the Month of an english calendar having less than 30 days = {February}; and

P = {x | x $\in$ I, $-$1 < x < 1} = {0}

So, the correct option is (A).