Given statement if [tex]xy[/tex] and [tex]yz[/tex] then [tex]zx[/tex] is describe by Syllogism.
" Statement is defined as the sentence which represents the condition either true or false but not both."
According to the question,
Given statement,
If [tex]xy[/tex] and [tex]yz[/tex] then [tex]zx[/tex]
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 [tex]xy[/tex] and [tex]yz[/tex]
Conclusion : then [tex]zx[/tex]
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 [tex]a =b , b=c[/tex] then [tex]a =c.[/tex]
This statement also represents syllogism,
If [tex]xy[/tex] and [tex]yz[/tex] then [tex]zx[/tex].
Hence, Option (D) is the correct answer.
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