# GATE Questions & Answers of First Order Logic

## What is the Weightage of First Order Logic in GATE Exam?

Total 3 Questions have been asked from First Order Logic topic of Discrete Mathematics subject in previous GATE papers. Average marks 2.00.

Consider the first order predicate formula $\varphi$:

$\forall x\lbrack(\forall z\;z\vert x\Rightarrow((z=x)\vee(z=1)))\Rightarrow\exists w\;(w>x)\wedge(\forall z\;z\vert w\Rightarrow((w=z)\vee(z=1)))\rbrack$ Here $'a\vert b'$ denotes that ‘$a$ divides $b$’, where $a$ and $b$ are integers. Consider the following sets:

S1.   {1,2,3, … , 100}

S2.   Set of all positive integers

S3.   Set of all integers

Which of the above sets satisfy $\varphi$?