GATE 2002
April 7, 2025GATE 2002
April 7, 2025GATE 2002
| Question 42 |
The binary relation S = ɸ (empty set) on set A = {1,2,3} is
| Neither reflexive nor symmetric | |
| Symmetric and reflexive | |
| Transitive and reflexive | |
| Transitive and symmetric |
Question 42 Explanation:
S = ɸ; A = {1,2,3}
A×S = {(ɸ,1), (ɸ,2), (ɸ,3), (1,ɸ), (2,ɸ), (3,ɸ)}
Not reflexive = (1,1), (2,2), (3,3) not there
Symmetric: if (a,b) is present then (b,a) is also present
Transitive: True; if (x,y), (y,z) then (z,x) is also present
A×S = {(ɸ,1), (ɸ,2), (ɸ,3), (1,ɸ), (2,ɸ), (3,ɸ)}
Not reflexive = (1,1), (2,2), (3,3) not there
Symmetric: if (a,b) is present then (b,a) is also present
Transitive: True; if (x,y), (y,z) then (z,x) is also present
Correct Answer: D
Question 42 Explanation:
S = ɸ; A = {1,2,3}
A×S = {(ɸ,1), (ɸ,2), (ɸ,3), (1,ɸ), (2,ɸ), (3,ɸ)}
Not reflexive = (1,1), (2,2), (3,3) not there
Symmetric: if (a,b) is present then (b,a) is also present
Transitive: True; if (x,y), (y,z) then (z,x) is also present
A×S = {(ɸ,1), (ɸ,2), (ɸ,3), (1,ɸ), (2,ɸ), (3,ɸ)}
Not reflexive = (1,1), (2,2), (3,3) not there
Symmetric: if (a,b) is present then (b,a) is also present
Transitive: True; if (x,y), (y,z) then (z,x) is also present