A relation R is defined on the set Z (set of all integers) by “aRb if and only if 2a + 3b is divisible by 5”, for all a, b ∈ Z. Is this relation a symmetric relation?
A relation R is defined on the set Z (set of all integers) by “aRb if and only if 2a + 3b is divisible by 5”, for all a, b ∈ Z. Is this relation a symmetric relation?
The correct option is A True
For any relation to be symmetric, if there is an element (a,b) then there should be an element (b,a). It means, from the given relation, if 2a+3b is divisible by 5, then 2b+3a is also divisible by 5. Is this true?
We will write 2a+3b as 5a+5b-(3a+2b). If we say that 2a+3b is divisible by 5, then 3a+2b should also be a multiple of 5, because 5a+5b is divisible by 5. We can also say that if 3a+2b is divisible by 5, then 5(a+b)- (3a+2b) or 2a+3b is also a multiple of 5. It means if there is an element (a,b) then there will be an element (b,a) in the given relation. => Symmetric.
True
For any relation to be symmetric, if there is an element (a,b) then there should be an element (b,a). It means, from the given relation, if 2a+3b is divisible by 5, then 2b+3a is also divisible by 5. Is this true?
We will write 2a+3b as 5a+5b-(3a+2b). If we say that 2a+3b is divisible by 5, then 3a+2b should also be a multiple of 5, because 5a+5b is divisible by 5. We can also say that if 3a+2b is divisible by 5, then 5(a+b)- (3a+2b) or 2a+3b is also a multiple of 5. It means if there is an element (a,b) then there will be an element (b,a) in the given relation. => Symmetric.
