Mathematical reasoning is an essential yet interesting part of JEE Main 2022, where you need to determine the truth value of a given statement. Mathematical reasoning (also called a science of proof) deals with the principles of reasoning.
Logical reasoning plays a major role in our day-to-day lives. For instance, a triangle has three sides. This statement is true. If we say a rectangle has 3 sides, then it would be false. This topic is covered under the JEE Main 2022 Maths carrying 4 marks. It is one of the easiest topics in the whole syllabus.
Therefore, in this blog, we will shed some light on JEE Main 2022 Maths reasoning with important topics for revision, and the significance of maths reasoning in JEE Main 2022 preparation.
JEE Main 2022 Maths Reasoning – Important Topics
The important topics for JEE Main 2022 Maths Reasoning are:
- Basic Logic Connectives
- Conditional Statement
- Biconditional Statement
- Validity of Statements
- Algebra of Statements
Types of Reasoning in Maths
There are a total of 7 types of reasoning in mathematics.
The topics comprise intuition, counterfactual thinking, backward induction, critical thinking, and abductive induction. But inductive and deductive reasoning are the 2 most used in mathematics to make decisions.
Maths Reasoning can be categorised mainly into 2 types:
- Inductive Reasoning
- Deductive Reasoning
In Inductive reasoning, the validity of the statement is checked by a set of rules and is generalised. It is not considered to fit in geometrical proofs.
Statement: The cost of 1 banana is Rs 10, and the cost of transporting it is Rs. 5. The sales price of 1 banana is Rs. 50.
Reasoning: From the above statement, it can be said that bananas will provide a good profit for the stores selling them.
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Deductive reasoning is the opposite of the principle of induction. Contrary to inductive reasoning, we apply the rules of a general case to a given statement and make it true for particular statements in deductive reasoning. The principle of mathematical induction is based on the concept of deductive reasoning.
Statement: Pythagorean Theorem applies to any right-angled triangle.
Reasoning: If triangle ABC is a right triangle, it will follow Pythagorean Theorem.
A statement is a mathematical expression that is either true or false, but not both simultaneously.
Properties of Statements
- A statement is an acceptable mathematical sentence.
- Any exclamatory sentences are not mathematical statements.
- An imperative sentence is not a valid mathematical statement.
- An interrogative sentence is not a valid mathematical statement.
- A sentence involving variables such as here, there, today, tomorrow, and yesterday or any pronouns is not a statement.
- Ambiguous (unclear) sentences are invalid in mathematics.
- A dog has four legs.
- Physics is an experimental subject.
- How old are you?
- How old are you? This statement is not clear, and we can’t decide whether it’s true or false.
- The statement should be either true or false.
The statements can be simple or compound.
If a statement cannot be further broken down into different statements or it is itself complete, then it is called a Simple Statement.
- A kite is not a rhombus.
- 11 is an odd number.
If a statement can further be broken down into simpler statements, forming two or more main statements, then it is called a Compound Statement.
For example, 20 is non-negative and a multiple of 5. This statement can be into two independent statements:
- 20 is non-negative.
- 20 is a multiple of 5.
Basic Logical Connectivities
A Logical Connective is a symbol used to connect two or more simple statements in such a manner that the resultant logic is a compound statement. Some of the common connectives are given below:
- Logical Negation
- Logical Conjunction (AND)
- Logical Disjunction (Inclusive OR)
- Logical Implication (Conditional)
- Logical Biconditional (Double Implication)
If a connective “if-then” is used to make the compound statement if p then q, it is a conditional statement. It is also called an implication and is written as p => q.
For example, If the laptop has a keyboard, then the clock has a needle.
Let p= laptop has a mouse and q= clock has a pendulum. The given statement is in the form p => q
Its contrapositive statement is ~q=>~p
The logic would be: If the clock has no pendulum, then the laptop has no mouse.
The Converse of a Conditional Statement
If p=>q is a conditional statement; then its converse is q=>p
Suppose the conditional statement is: If the laptop has a mouse, then the clock has a pendulum.
Then, its converse would be obtained as: If the clock has a pendulum, then the laptop has a mouse.
A biconditional statement is a logical statement that includes the phrase “if and only if,” sometimes abbreviated as “iff.” It has many several different forms:
- p iff q
- p if and only if q
Consider this statement: You are breathing if and only if you are alive.
This is p↔q
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Validity of Statements
The validity of statements refers to the process of verifying when the given statement is true and not true.
For example: If p and q are 2 logical statements, then to show the statement “p or q” is true, we need to show that either one of them is true, i.e., either statement p is true, or statement q is true.
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Algebra of Statements
In algebra, a statement is a sentence that is either true or false but can’t be both simultaneously. These mathematical statements may consist of digits, words, and symbols.
For example, ‘The square root of 25 is 2’ is a mathematical statement and eventually a false statement.
Benefits of solving Maths reasoning problems in JEE Main 2022 Preparation
Keep in mind that well-developed logical thinking skills not only enhance your analytical skills but also boosts problem-solving skills, concepts grasping power, and reasoning skills. It is important to understand what logical thinking means and how it affects our daily lives.
To have a better understanding, you can look at the positive effects below.
- Rational students can easily correlate events and objects.
- Their chance of making mistakes is likely less.
- Students with strong logical thinking skills are successful as they can establish cause and effect relations with a rational perspective.
- They are likely to be more successful at work because they develop the right working and problem-solving strategies.
Therefore, learn JEE Main 2022 Maths reasoning skills through extensive practice and visual learning. Moreover, we have curated a video on Maths reasoning for you to deepen your understanding of the subject and topics with some awesome examples from our daily lives so that you can think logically in every situation. Now, efficiently train your brain and ace the JEE mains 2022 Maths reasoning.
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