in Mathematical Logic
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Show that (p → q) ∧ (q → r) and (p → r) is a logically equivalent to each other
in Mathematical Logic
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A is logically equivalent to B if A→B and B→A both are tautology.

Rule- If A^B→C is valid, if we make C false then at least one of A and B, must be false.

Using this rule if you check, then you will find

(p → q) ∧ (q → r)→(p → r) is tautology.

(p → r)→(p → q) ∧ (q → r) is not tautology.

So not equivalent.
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They are not logically equivalent to each other..Reason is:

(p → q) ∧ (q → r)→(p → r) is tautology.

but

(p → r)→(p → q) ∧ (q → r) is not tautology.
(p=0,q=1,r=0)

So not equivalent to each other
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