Introduction
In this blog, we will discuss Conditional and biconditional statements and discuss some terms related to them. But before we discuss this topic in detail, we should first look at some of the basic terminologies related to this topic.
Compound Statement: A compound statement is formed by combining two basic assertions with conditional terms such as 'and,' 'or,' 'not,' 'if,' 'then,' and 'if and only if.'
Compound Proposition: A compound proposition is a statement made up of two propositions connected by the connective "If...then...". p→q is denoted.
Conditional Statements
Conditional Operation occurs when a compound statement is generated by two basic assertions linked by the phrase 'if and then.' A conditional statement can be broken down into two statements: a hypothesis, and the other is a conclusion statement. For example, consider the following statement: "If you practice DSA on Coding Ninjas Studio, then you clear any interview of FAANG." This statement is made up of two simple statements:
p:" If you practice DSA on Coding Ninjas Studio."
q: "then you can clear any interview of FAANG."
Here p is called a hypothesis, and q is a conclusion statement.
Remember that hypothesis always starts with "if," and conclusion always starts with "then."
According to the original statement, if p is true, then only q is true, or we can say in layman terms that if p then q. This can also be rephrased as p implies q, p→q.
The truth table for Conditional Operation:
P |
Q |
P → Q |
T |
T |
T |
T |
F |
F |
F |
T |
T |
F |
F |
T |
Now let us discuss some example statements to get a better idea of conditional statements.
Case 1 (True implies True)
If p and q both are true, then p→q is true.
For instance: If 1+10 = 11, then the moon will revolve around the earth.
Here p is "If 1+10 = 11" and q is" then the moon will revolve around the earth." As we can see here, p is true, and q is also true; therefore, p→q is also true.
Case 2 (True implies False)
If p is true and q is false, then p→q is false.
For instance: If it rains, then I will carry an umbrella.
Here p is" If it rains" and q is "then I will carry an umbrella." In other words, we can rephrase this statement as to when it is raining, and then I will be carrying an umbrella. Now there might be someday when it is raining (true), and I would forget to carry an umbrella (false), then this condition of p→q would be false.
Case 3 (False implies both True and False)
Whether q is false or not, If p is false, then p→q is true.
For instance: If chocolate is made of gold, then Neil Armstrong was the first person to step on the moon.
Here p is "If chocolate is made of gold" and q is "then Neil Armstrong was the first person to step on the moon." As we can see, p is false here, but q is true. Therefore, statement p→q is true.