In 2022, India’s toughest engineering entrance exam JEE Main will be conducted by JEE Apex Board (JAB). The National Testing Agency will assist JAB in conducting the exams. According to the latest update, JEE 2022 will begin on June 23. Students can download the exam city intimation slip from the official website of the National Testing Agency. Since a large number of students appear for this national-level test, cracking the JEE is not possible in an easy manner. It requires too much effort and learning to ace the exam. Students should be familiar with the syllabus before starting the preparation.
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Mathematical reasoning is very important for any engineering entrance exam. Mathematical reasoning is a branch of mathematics where we find out the truth values for the given statements. Inductive reasoning and deductive reasoning are the major types of reasoning in mathematics. We use three techniques for deducing new statements. These are the negation of statements, counter statements and contradiction methods. In this article, we will discuss negation, solved examples etc.
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Logical Operations
The logical operations in mathematical reasoning are those that connect or join simple statements. Given below are the various types of logical operations.
- Conjunction operation
- Disjunction operation
- Conditional operation
- Biconditional operation
- Negation or NOT operation
Let A and B be two statements. “A and B” is the conjunction of the statements A and B. We represent it by A∧B. The conjunction statement A∧B is true only when both A and B are true. Disjunction is denoted by the symbol ∨. The statement for disjunction is “A or B”. We denote it by A∨B. The statement A∨B is correct only when at least one of A or B is true.
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What is Negation?
Negation of a statement means denial of the given statement. We can also say that negation gives the opposite of the statement. It is represented by the symbol, ~. For example, consider the statement P: Rita is not in Class 10. Then negation of P, ~P: Rita is in Class 10. Another example; let Q: 11 is a prime number. Then negation of Q, ~Q: 11 is not a prime number.
Combination and permutation
Permutation and combination is an important topic for any engineering entrance exam. We use combinations when the order of selection doesn’t matter. The combination formula is given by nCr = n!/r! (n-r)!. Note that the number of combination of n different things taking nothing at all is 1. Counting combination is counting the number of ways in which all or some of the objects are selected at a time. Selecting no item means we are leaving behind all the things. We can do it in only one way. Therefore, we can say that nC0 = 1.
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Students can expect tricky questions from permutation and combination. They often get confused with permutation and combination. So they should learn the basic concepts properly so that they can easily solve the problems from this topic. Log on to BYJU’S to learn mathematical reasoning, previous years’ solved question papers on mathematical reasoning, important notes, etc.
