The document discusses propositional logic, defining propositions as expressions that can be true or false, and illustrating this with examples. It explains logical connectives as the symbols used to combine propositions and discusses logical equivalence, where two statements have the same truth value. The document provides references for further study on logical equivalences.

2. From Propositional Logic

3. Example 2
References
What is Proposition
What is Logical Connectives
Logical Equivalence
Example 1

4. An expression consisting of some letter, words and
symbols is called a propositional if it is True or False.
If the proposition is True, it is denoted by ‘T’ and if it is
False , it is denoted by ‘F’.
For example,
a. The Sun Rises in the East [ T ]
b. 2 > 5 [ F ]

5. The particular words and symbols used
to join two or more proposition into a
single composite form is called logical
connectives.
For Example,
Delhi is The Capital of India
and 2+2 = 4 [ T ]
The above proposition is a combination
of two propositions joined by a
connective ‘and’

7. Two statements are said
to be logically equivalent
(or equivalent) if they
have the same truth value
for every row of the truth
table, that is if x y is a
tautology.
Symbolically, x y.

8. Show That,

9. Show That, p q (p q)^ (q p)

10. https://www.slideshare.net/fvsandoval/formal-logic-logical-
equivalence
https://math.libretexts.org/Courses/Monroe_Community_College
/MTH_220_Discrete_Math/2%3A_Logic/2.5%3A_Logical_Equiva
lences
https://en.wikipedia.org/wiki/Logical_equivalence