Given, A={1,2,3,4} and R={(a,b):a+b≤4}.
a) The elements of the relation R is, R={(1,1),(1,2),(1,3),(2,1),(2,2),(3,1)}.
b)
i) R is not reflexive, since (3,3)∈/R
ii) R is not transitive, since (2,1)∈R,(1,3)∈R, but (2,3)∈/R
iii) R is not anti-symmetry, since (1,2)∈R,(2,1)∈R, but 1=2.
iv) For each (a,b)∈R , we have (b,a)∈R. Hence, R is symmetry.
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