Let A and B be two sets and n(A)=4 and n(B)=2. If number of onto functions from A to B is p and number of one-one functions from B to A is q then (p+q) equals

Question

Let A and B be two sets and n(A)=4 and n(B)=2. If number of onto functions from A to B is p and number of one-one functions from B to A is q then (p+q) equals (A) 26 (B) 28 (C) 32 (D) 122

Tardigrade Admin · Accepted Answer

Number of onto function from A to B is =24-2 ⇒ p=14 <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/4ac714ddaf79af8623fe0cd6c97f1e97-.png" /> Number of one-one function from B to A is, q=4 × 3=12 Aliter: q = 4 C 2 × C 2 =6 × 2=12

Q. Let $A$ and $B$ be two sets and $n (A) = 4$ and $n (B) = 2$ . If number of onto functions from $A$ to $B$ is $p$ and number of one-one functions from $B$ to $A$ is $q$ then $(p + q)$ equals

26

28

32

122

Number of onto function from A to B is $= 2^{4} - 2 \Rightarrow p = 14$

Number of one-one function from B to A is, $q = 4 \times 3 = 12$
Aliter :
$q =^{4} C_{2} \times C_{2}$
$= 6 \times 2 = 12$

Q. Let A and B be two sets and n(A)=4 and n(B)=2. If number of onto functions from A to B is p and number of one-one functions from B to A is q then (p+q) equals

26

28

32

122

Number of onto function from A to B is =24−2⇒p=14 Number of one-one function from B to A is, q=4×3=12 Aliter : q=4C2​×C2​ =6×2=12

Q. Let $A$ and $B$ be two sets and $n (A) = 4$ and $n (B) = 2$ . If number of onto functions from $A$ to $B$ is $p$ and number of one-one functions from $B$ to $A$ is $q$ then $(p + q)$ equals

Number of onto function from A to B is $= 2^{4} - 2 \Rightarrow p = 14$

Number of one-one function from B to A is, $q = 4 \times 3 = 12$
Aliter :
$q =^{4} C_{2} \times C_{2}$
$= 6 \times 2 = 12$