Question

4. [3 marks) Let S = {a,b,c}. Find the number of partial orders on S.

Answer 1

8

Explanation:

Partial order of a set:A relation R on set A is called partial order if it is reflexive,anti-symmetric and transitive.The set together with partial order R is called partial ordered set.

Partial order is the collection of subsets of set A.

A=P(S)

Power set of S=P(S)={
`\phi`,{a},{b},{c},{a,b},{b,c},{a,c},{a,b,c}}

Partial order on S =P(S)=
`2^3`

Partial order=8

Hence, the partial order on S=8