Dear students,

Today we discuss the simplest topic from Paper – I i.e. Logic. Here you
should first know the meaning of the word ‘Statement’. You have to remember
five logical connectives with their symbols and truth tables. The conditional i.e.
implication can be remembered as:
“If there is a cause then it must be accompanied by the effect!
i.e. implication p → q is false only when p is true and q is false.

If p → q is a conditional statement, then
i. q → p is its converse.
ii. ~ p → ~ q is its inverse.
iii. ~ q → ~ p is its contrapositive.
It can be verified that
p → q ≡ ~ q → ~ p and q → p ≡ ~ p → ~ q

A statement pattern which has all the entries in the last column of its truth
table as ‘T’ is a tautology and if all entries are ‘F’ then it is a fallacy or
contradiction.
A statement pattern which is neither a tautology nor a fallacy is a
contingency.

Note that while obtaining negation do not just open the brackets !
e.g. ~ ( p → q ) ≠ ~ p → ~ q
but ~ ( p → q ) ≡ p ∧~ q

You have to remember the rules.

Two compound statements S1 and S2 are said to be duals of each other if
one can be obtained from the other by interchanging ∧ and ∨.
For Example
~ ( p∧ q ) ≡ ~ p∧ ~ q and

~(p∧q) ≡ ~p∧~q

are duals of each other.

They are also called as De Morgan’s Laws.

Logic can be used to select the right positions and the number of switches
in an electric circuit.

In electric circuits the notation ‘1’ is used if the switch is closed i.e. ON
and ‘0’ is used if the switch is open i.e. OFF.
Clearly, switches in parallel correspond to disjunction and in series
correspond to conjunction.
Finally, if ‘t’ denotes tautology and ‘c’ denotes contradiction, then

• p ∨ t  ≡  t
• p ∧ t  ≡  p
• p ∨ c  ≡ p
• p ∧ c  ≡  c

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Wish you a Very Happy Diwali and a Prosperous New Year ahead !

- Ranade Sir
www.ednexa.com