Answer:
A.If[tex](p\implies q)\;and \;(q\implies r)[/tex],then [tex]p\implies r[/tex].
Step-by-step explanation:
We have to find the which statement illustrate the law of syllogism.
Law of syllogism: Premise: if p then q
Premise:If q then r.
Conclusion:If p then r.
It is like transitive property of equality.
A.If[tex](p\implies q)\;and \;(q\implies r)[/tex],then [tex]p\implies r[/tex].
It is true by definition of law of syllogism.
B.If[tex](p\implies q)\;and \;(q\implies p)[/tex],then [tex]p\implies r[/tex].
It is not true by definition of syllogism.
C.If[tex](p\implies q)\;and \;(p\implies r)[/tex],then [tex]q\implies r[/tex]
It is not true by definition of syllogism.
D.If[tex]p\implies r)\;and \;(q\implies r)[/tex],then [tex]p\implies r[/tex].
It is not true by definition of law of syllogism.
Answer:A
