Question

if p ={1,3}, q={2,3,5}, find the no. of relations from p to q

Answer 1

✪ᴀɴsᴡᴇʀ✪

• $\boxed{\bf{Number\:of\:Relation\:is\:2^6}}$

★ᴇxᴘʟᴀɪɴᴀᴛɪᴏɴ★

Here,

$\:\:\:\:\: n(p) = 2, n(q) = 3$

So,

$\to n(p\times q) = n(p) \times n(q)$

$\to n(p\times q) = 2 \times 3$

$\to n(p\times q) = 6$

Any subset of $\bf{p \times q}$ is a relation from $\bf{p}$ to $\bf{q}$ . So

⇒ No. of relation

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:$ = No. of subset of $p\times q$

⇒ No. of relation = $2^{n(p\times q)}$

⇒ No. of relation = $2^{6}$