Q 1. Prove that the statement:
If (a>b) then swap(a, b) else null;
arranges a and b in non-decreasing order.
Q 2. (Challenge) Prove that the statements:
If (a>b) then swap(a, b) else null;
If (b>c) then swap(b, c) else null;
If (a>b) then swap(a, b) else null;
arrange a, b and c in non-decreasing order.
1)
Consider a=5 and b=10.
Check If(a>b)
5>10
The condition is false.
Do nothing.
Therefore, a>b.
Hence, the value of a and b are in non-decreasing order.
2)
Consider a = 5, b = 10 and c = 1.
Check
If(a>b)
5>10
The condition is false.
Do nothing.
If(b>c)
10>1
The condition is True.
Swap b and c.
Therefore, b = 1 and c =10
If(a>b)
5>1
The condition is True.
Swap a and b.
Therefore, a = 1 and b =5.
Therefore, a < b <c.
Hence, the value of a, b, and c are in non-decreasing order.
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