Conjunction

Logical reasoning is one of the important skill that is used in all the fields such as science, engineering and even in our daily life activities. It is also used in mathematical problem-solving strategies. One can easily get the conclusion using the mathematical principles and the given facts. We know that there are different logical connections are used in Maths to solve the problem. The commonly used logical connectives are:

  • Negation
  • Conjunction
  • Disjunction
  • Implication
  • Equivalence

In this article, let us discuss in detail about one of the connectives called “Conjunction” with its definition, rules, truth table, and examples.

Conjunction in Maths

A conjunction is a statement formed by adding two statements with the connector AND. The symbol for conjunction is ‘∧’ which can be read as ‘and’. When two statements p and q are joined in a statement, the conjunction will be expressed symbolically as p∧q. If both the combining statements are true then this statement will be true otherwise, it is false.

Conjunction

Rules for a Conjunction

  • The conjunction statement will only be true if both the combining statements are true otherwise, the disjunction is false.
  • It is similar to an AND gate which is utilized under the topic Gate logic.
  • The definition is stated as let p and q be the two statements. The compound statement p ∧ q is called as the conjunction of p and q.
  • The symbol “∧” that denotes the conjunction is called as “and” which is the logical connective.

Conjunction Truth Table

P Q P ∧ Q
T T     T
T F     F
F T     F
F F     F

In this table, we can say that the conjunction is true only when both P and Q are true. If they are not then the conjunction statement will be false.

Conjunction Examples

Example 1:

Let r: 5 be a rational number and s: 15 be a prime number. Is it conjunction?

Solution:

Given that r: 5 is a rational number. This proposition is true.

s: 15 is a prime number. This proposition is false as 15 is a composite number.

Therefore, as per the truth table, r and s is a false statement.

So, r ∧ s = F

Example 2:

Let a: x is greater than 9 and b: x be a prime number. Is it conjunction?

Solution:

Since x is a variable whose value we don’t know. Let us define a range for a and b.

To find the range let us take certain values for x;

When x= 6: a is false so is b hence a ∧ b is false.

When x= 3: a is false but b is true. But still, a ∧ b is false.

When x= 10: a is true but b is false. But still, a ∧ b is false.

When x= 11: a is true and b is true. Hence, a ∧ b is true.

Hence the conjunction a and b is only true when x is a prime number greater than 9.

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