Given statement if \(xy\) and \(yz\) then \(zx\) is describe by Syllogism.
What is statement?
" Statement is defined as the sentence which represents the condition either true or false but not both."
According to the question,
Given statement,
If \(xy\) and \(yz\) then \(zx\)
A. Contrapositive : It represents the conditional statement " If p then q and if ~ q then ~p".
Option A is not the correct answer.
B. Converse : In this case hypothesis and conclusion of statement get interchange.
Hypothesis : If \(xy\) and \(yz\)
Conclusion : then \(zx\)
Converse of this not possible.
Option B is not the correct answer.
C. Inverse : Opposite of mathematical operation.
This is conditional statement not representing inverse.
Option C is not the correct answer.
D. Syllogism : Syllogism reflects the transitive property, if \(a =b , b=c\) then \(a =c.\)
This statement also represents syllogism,
If \(xy\) and \(yz\) then \(zx\).
Hence, Option (D) is the correct answer.
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