Question:

The logically equivalent preposition of $p \Leftrightarrow q$ is

Updated On: Jul 7, 2022
  • $( p \Rightarrow q) \wedge (q \Rightarrow p)$
  • $p \wedge q $
  • $(p \wedge q) \vee (q \Rightarrow p)$
  • $(p \wedge q) \Rightarrow (q \vee p)$
Hide Solution
collegedunia
Verified By Collegedunia

The Correct Option is A

Solution and Explanation

$(p \Rightarrow q) \wedge ( q \Rightarrow p)$ means $p \Leftrightarrow q$
Was this answer helpful?
0
0

Top Questions on Statements

View More Questions

Concepts Used:

Statements

A statement is a sentence that is either true or false, but not both true and false simultaneously.

Types of Statements:

Simple Statement

  • If a statement cannot be further broken down into various statements, or in simpler words if it is concrete by itself, it is called a Simple Statement.
  • Examples include:
    • A kite is not a rhombus.
    • 15 is an odd number.

Compound Statement

  • If a statement can further be broken down into simpler statements so that from a main statement, we can yield more than one statement, then it is called a Compound Statement.
  • Consider the statement “10 is non-negative and a multiple of 5” which can be broken down into the statements: “10 is non-negative” and “10 is a multiple of 5”.

If-Then Statements

  • If we encounter an if-then statement i.e. ‘if a then b’, then by proving that a is true, b can be proved to be true or if we prove that b is false, then a is also false.
  • If we encounter a statement which says ‘a if and only if b’, then we can give reason for such a statement by showing that if a is true, then b is also true and if b is true, then a is also true.
  • Example:
    • a: 8 is multiple of 64
    • b: 8 is a factor of 64

Since one of the given statements i.e. a is true, therefore, a or b is true.