Solution:
Let's write the pairs (x,y) in R
‌(0,3),(1,3),(2,3),(3,3),(4,3),(5,3),(3,0),(3,1),(3,2),(3,4),(3,5),(0,4),(1,4),(2,4),(4,4),(5,4),(4,0),(4,1),(4,2),(4,5)
There are total 20 pairs
If (x,y)∈R, then max(x,y)∈{3,4}
This means, max(y,x)∈{3,4}. So, (y,x)∈R.
Thus R is symmetric
‌ Since ‌max(5,5)=5∉{3,4},(5,5)∉R
Thus R is not reflexive
(3,4)∈R&(4,2)∈R,‌ but ‌(3,2)∉R,2∉{3,4}
Thus, R is not transitive
Therefore, only S2 is true
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