Relations
Question 1 |
The less-than relation, <, on reals is
a partial ordering since it is asymmetric and reflexive | |
a partial ordering since it is antisymmetric and reflexive | |
not a partial ordering because it is not asymmetric and not reflexive | |
not a partial ordering because it is not antisymmetric and reflexive
| |
none of the above |
Question 1 Explanation:
Relation < is:
1) not reflexive
2) irreflexive
3) not symmetric
4) Asymmetric
5) Antisymmetric
1) not reflexive
2) irreflexive
3) not symmetric
4) Asymmetric
5) Antisymmetric
Question 2 |
Amongst the properties {reflexivity, symmetry, anti-symmetry, transitivity} the relation R = {(x,y) ∈ N2 | x ≠ y } satisfies __________.
symmetry |
Question 2 Explanation:
It is not reflexive as xRx is not possible.
It is symmetric as if xRy then yRx.
It is not antisymmetric as xRy and yRx are possible and we can have x≠y.
It is not transitive as if xRy and yRz then xRz need not be true. This is violated when x=x.
So, symmetry is the answer.
It is symmetric as if xRy then yRx.
It is not antisymmetric as xRy and yRx are possible and we can have x≠y.
It is not transitive as if xRy and yRz then xRz need not be true. This is violated when x=x.
So, symmetry is the answer.
There are 2 questions to complete.