First slide

Introduction to mathematical reasoning

Question

The negation of the following statement P: Neha lives in Ludhiana or she lives in Gurudaspur.

Easy

A

Neha does not live in Ludhiana or she does not live in Gurudaspur.
B

Neha does not live in Ludhiana and she does not live in Gurudaspur
C

Neha does not live in Punjab.
D

None of these.

Solution

Let p and q be the statements defined as follows
p : Neha lives in Ludhiana
q : Neha lives in Gurudaspur.
The statement P is
$P : p \lor q$
Negation of p is
$~ P :\sim (p \lor q)$
or $~ P : (~ p) \land (~ q) [∵\sim (p \lor q) \equiv (~ p) \land (~ q)]$
Thus, negation of P is given by $(b)$

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