MATHEMATICAL REASONING – JEE Main Concepts Part 2 – By Nitesh Choudhary - Videos

Mathematical Reasoning JEE Main Lecture Playlist Link

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In this video, we will cover some very important laws related to logical operators conjunction and disjunction in mathematical reasoning, based on which two questions came in JEE Main in year 2014, 2015 and 2016.
ALGEBRA OF STATEMENTS
Idempotent laws. If p is any statement then:
p∨p≡p
p∧p≡p
Complement laws. If p is any statement then:
p∨~p≡t
p∧~p≡f
~~p≡p
~t≡f,~f≡t
Where, t and f are respectively some tautology and fallacy in terms of the statement p.
Identity laws. If p is any statement then:
p∧t≡p
p∧f≡f
p∨t≡t
p∨f≡p
Where, t and f are respectively some tautology and fallacy in terms of the statement p.
Commutative laws. If p and q be any two statements, then:
p∧q≡q∧p
p∨q≡q∨p
De Morgan’s laws. If p and q be any two statements, then:
~(p∧q)≡~p∨~q
~(p∨q)≡~p∧~q
Associative laws. If p, q and r be any three statements, then:
(p∧q)∧r≡p∧(q∧r)
(p∨q)∨r≡p∨(q∨r)
Dissociative laws. If p, q and r be any three statements, then:
p∧(q∨r)≡(p∧q)∨(p∧r)
p∨(q∧r)≡(p∨q)∧(p∨r)
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Questions Discussed
JEE Main 2014 Online
The proposition: ~(p∨~q)∨~(p∨q) is logically equivalent to
(A) p (B) q (C) ~p (D) ~q
[Answer (C)]

JEE Main 2016
The Boolean expression (p∧~q)∨q∨(~p∧q) is equivalent to
(A) p∧q (B) p∨q (C) p∨~q (D) ~p∧q
[Answer (B)]
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TRY YOURSELF QUESTIONS
JEE Main 2015
The negation of ~s∨(~r∧s) is equivalent to
(A) s∧~r (B) s∧(r∧~s) (C) s∨(r∨~s) (D) s∧r
[Answer (D)]

Question 2
The proposition: p∧(~(~p∨q))∨(p∧q) is logically equivalent to
(A) p (B) q (C) ~p (D) ~q
[Answer (A)]
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Some Important Links are given below:

STATISTICS IIT JEE Concepts Playlist Link

Sum of Series IIT JEE Concepts Playlist Link

Permutation and Combination IIT JEE Concepts Playlist Link

Binomial Theorem IIT JEE Concepts Playlist Link

Complex Numbers Maximum and Minimum Value IIT JEE Concepts Playlist Link

Physics Formulae Revision Playlist Link


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