Q3 of 107 Page 24

consider the binary operation ∧ on the set {1, 2, 3, 4, 5} defined by a ∧ b = min {a, b}. Write the operation table of the operation ∧.

The binary operation ^ on the set {1, 2, 3, 4, 5} is defined as a^b = min {a, b}

for a, b ϵ {1, 2, 3, 4, 5}


Therefore, the operation table of the given operation ^ can be given as:




















































^



1



2



3



4



5



1



1



1



1



1



1



2



1



2



2



2



2



3



1



2



3



3



3



4



1



2



3



4



4



5



1



2



3



4



5



More from this chapter

All 107 →
2

For each operation ∗ defined below, determine whether ∗ is binary, commutative or associative.

On Z+, define a ∗ b = ab

 2

For each operation ∗ defined below, determine whether ∗ is binary, commutative or associative.

On R – {–1}, define a ∗ b =

4

Consider a binary operation ∗ on the set {1, 2, 3, 4, 5} given by the following multiplication table (Table 1.2).

(i) Compute (2 ∗ 3) ∗ 4 and 2 ∗ (3 ∗ 4)


(ii) Is ∗ commutative?


(iii) Compute (2 ∗ 3) ∗ (4 ∗ 5).


(Hint: use the following table)


Table 1.2


 5

Let ∗′ be the binary operation on the set {1, 2, 3, 4, 5} defined by a ∗′ b = H.C.F. of a and b. Is the operation ∗′ same as the operation ∗ defined in Exercise 4 above? Justify your answer.