Set, Relations and FunctionsPYQ Nov. 19Question 1961 of 217
All Questions

If A={a,b,c,d}\displaystyle A = \{a, b, c, d\}, B={p,q,r,s}\displaystyle B = \{p, q, r, s\} which of the following relation is a function from A\displaystyle A to B\displaystyle B

Options

AR1={(p,a),(b,q),(c,s)}\displaystyle R_1 = \{(p,a), (b,q), (c,s)\}
BR2={(p,a),(b,r),(d,s)}\displaystyle R_2 = \{(p,a), (b,r), (d,s)\}
CR3={(b,p),(c,s),(b,r)}\displaystyle R_3 = \{(b,p), (c,s), (b,r)\}
DR4={(a,p),(b,r),(c,q),(d,s)}\displaystyle R_4 = \{(a,p), (b,r), (c,q), (d,s)\}
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option d — R4={(a,p),(b,r),(c,q),(d,s)}\displaystyle R_4 = \{(a,p), (b,r), (c,q), (d,s)\}

All Options:

  • AR1={(p,a),(b,q),(c,s)}\displaystyle R_1 = \{(p,a), (b,q), (c,s)\}
  • BR2={(p,a),(b,r),(d,s)}\displaystyle R_2 = \{(p,a), (b,r), (d,s)\}
  • CR3={(b,p),(c,s),(b,r)}\displaystyle R_3 = \{(b,p), (c,s), (b,r)\}
  • DR4={(a,p),(b,r),(c,q),(d,s)}\displaystyle R_4 = \{(a,p), (b,r), (c,q), (d,s)\}

Detailed Solution & Explanation

We are given sets A={a,b,c,d}\displaystyle A = \{a, b, c, d\} and B={p,q,r,s}\displaystyle B = \{p, q, r, s\}.
A relation from A\displaystyle A to B\displaystyle B is a function if every element of the domain A\displaystyle A appears exactly once as the first component in the ordered pairs of the relation.
Let's test each option:
- **Option A**: R1={(p,a),(b,q),(c,s)}\displaystyle R_1 = \{(p,a), (b,q), (c,s)\}. The first component p\displaystyle p does not belong to the domain A\displaystyle A. So R1\displaystyle R_1 is not a relation from A\displaystyle A to B\displaystyle B.
- **Option B**: R2={(p,a),(b,r),(d,s)}\displaystyle R_2 = \{(p,a), (b,r), (d,s)\}. The first component p∉A\displaystyle p \notin A. So R2\displaystyle R_2 is not a relation from A\displaystyle A to B\displaystyle B.
- **Option C**: R3={(b,p),(c,s),(b,r)}\displaystyle R_3 = \{(b,p), (c,s), (b,r)\}. The element b\displaystyle b is mapped to two different values p\displaystyle p and r\displaystyle r. Also, elements a\displaystyle a and d\displaystyle d have no images. So R3\displaystyle R_3 is not a function.
- **Option D**: R4={(a,p),(b,r),(c,q),(d,s)}\displaystyle R_4 = \{(a,p), (b,r), (c,q), (d,s)\}. Every element of A={a,b,c,d}\displaystyle A = \{a, b, c, d\} appears exactly once as the first component, and all second components belong to B\displaystyle B. Therefore, R4\displaystyle R_4 is a function.
Hence, **Option D** is the correct answer.

More Questions from Set, Relations and Functions

If A={1,2,3,4,5}\displaystyle A = \{1, 2, 3, 4, 5\}, B={2,4}\displaystyle B = \{2, 4\} and C={1,3,5}\displaystyle C = \{1, 3, 5\} then (A−C)×B\displaystyle (A - C) \times B is:

If f(x)=x2−5\displaystyle f(x)=x^2-5, evaluate f(3)\displaystyle f(3), f(−4)\displaystyle f(-4), f(5)\displaystyle f(5), and f(1)\displaystyle f(1).

Out of a group of 20\displaystyle 20 teachers in a school, 10\displaystyle 10 teach Mathematics, 9\displaystyle 9 teach Physics and 7\displaystyle 7 teach Chemistry. 4\displaystyle 4 teach Mathematics and Physics but none teach both Mathematics and Chemistry. How many teach Chemistry and Physics; how many teach only Physics?

If A={1,2,3,4,5,7,8,9}\displaystyle A = \{1, 2, 3, 4, 5, 7, 8, 9\} and B={2,4,6,7,9}\displaystyle B = \{2, 4, 6, 7, 9\} then how many proper subset of A∩B\displaystyle A \cap B can be created?

The number of subsets of the set {0,1,2,3}\displaystyle \{0, 1, 2, 3\} is:

If f(x)=x2+x−1\displaystyle f(x) = x^2+x-1 and 4f(x)=f(2x)\displaystyle 4f(x) = f(2x), then find the value of 'x'.

Ready to Master Set, Relations and Functions?

Practice all 217 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free