The number of binary operations on the set a, b are

Question

The number of binary operations on the set a, b are (A) 10 (B) 16 (C) 20 (D) 8

Tardigrade Admin · Accepted Answer

A binary operation * on a, b is a function from a, b × a, b arrow a, b i.e., * is a function from (a, a),(a, b),(b, a),(b, b) arrow a, b . Hence, the total number of binary operations on the set a, b is 24 i.e., 16 .

Q. The number of binary operations on the set ${a, b}$ are

10

16

20

8

A binary operation * on ${a, b}$ is a function from ${a, b} \times {a, b} \to {a, b}$
i.e., $*$ is a function from ${(a, a), (a, b), (b, a), (b, b)} \to {a, b}$ .
Hence, the total number of binary operations on the set ${a, b}$ is $2^{4}$ i.e., 16 .

Q. The number of binary operations on the set {a,b} are

10

16

20

8

A binary operation * on {a,b} is a function from {a,b}×{a,b}→{a,b} i.e., ∗ is a function from {(a,a),(a,b),(b,a),(b,b)}→{a,b}. Hence, the total number of binary operations on the set {a,b} is 24 i.e., 16 .

Q. The number of binary operations on the set ${a, b}$ are

A binary operation * on ${a, b}$ is a function from ${a, b} \times {a, b} \to {a, b}$
i.e., $*$ is a function from ${(a, a), (a, b), (b, a), (b, b)} \to {a, b}$ .
Hence, the total number of binary operations on the set ${a, b}$ is $2^{4}$ i.e., 16 .