LOGICAL CONNECTIVES  IBPS PO /clerks/SSC/IAS
Nowadays in IBPS exams questions are framed to match earlier CAT LEVEL. please go through this.
Logical Connectives
A Logical
Connective (also called a logical operator) is a symbol or a word
which is used to connect two or more sentences. Each logical connective can be
expressed as a truth function.
Logical connectives
 NOT (Negation)
 AND (Conjunction)
 EITHER OR (Disjunction)
 IFTHEN (Material Implication)
In
logical reasoning, we deal with statements that are essentially sentences in
English language. However, factual correctness is not important. We are only
interested in logical truthfulness of the statements. We can represent simple
statements using symbols like p and q. When simple statements are combines
using logical connectives, compound statements are formed.
Negation  NOT
Negation
is the opposite of a statement. For example,
 Statement:
It is raining.
 Negation:
It is NOT raining.
Disjunction  EITHER OR
When two statements
are connected using OR, at least one of them is true. For example,
 Either p or q: p alone is true; q alone is true;
both are true
In
such situation, valid inference is If p did not happen, then q must happen. And
If p did not happen, then p must happen.
Conjunction  AND
When
two statements are connected using AND, both statements have to be true for
compound statement to be true.
 p and q: p
should be true as well as q should be true
Material Implication  IF THEN
If
p, then q (p > q): It is read as p implies q. It means that if we know p
has occured, we can conclude that q has occured. In such situations, only valid
inference is "If ~q, then ~p"; If q did not happen, then p did not
happen.
Negation of Compound Statements
 Negation
(p OR q) is same as Negation p AND Negation q
 Negation
(p AND q) is same as Negation p OR Negation q
 Negation
(p > q) is same as Negation p > Negation q
Logical Connectives Summary Table
Given

Similar as

Valid Inference

If p, Then
q

If ~q,
Then ~p


Only If p,
Then q

If q, Then
p

If ~p,
Then ~q

Unless p,
Then q

If ~p,
Then q

If ~q,
Then p

Either p
or q

If ~p,
Then q


If ~q,
Then p

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