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JEE Main 2026 Preparation: Question Papers, Solutions, Mock Tests & Strategy Unacademy » JEE Study Material » Mathematics » Statement and logical operation
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Statement and logical operation

On mathematical statements, a logical operator (or connective) is a word or combination of words that joins one or more mathematical statements to form a new mathematical statement.

Table of Content
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A compounded logical statement has at least one of the logical operations (or connectives) negation, disjunction, or conjunction in it. There are no logical operations in a basic (also known as atomic) logical statement. A truth table in Boolean algebra is a table that shows the truth value of a statement formula for all conceivable combinations of component statement truth values. A statement is a declarative sentence that contains only one of the two truth values. True and false truth values are symbolized by the letters T and F, respectively.

Logical operators

While binary true/false signals are the fundamental basis of all digital computers, logical operators work on logical true (1) or false (0) arguments. They are very significant to ECE students. The logical operators are frequently used to aid in the creation of a test expression that regulates programme flow. Because they produce a Boolean answer or value when evaluated, this form of expression is also known as a Boolean expression. There are three popular logical operators that manipulate other Boolean operands to produce a Boolean value (s).

If you’re familiar with digital gates, you’ll recognize the following digital logic symbols:

  • AND
  • OR
  • NOT

As an example, the situation where you need to verify the accuracy of numbers in a big collection of electronically collected position measurements. If the sensor returns an error condition, these numbers should all be nonnegative integers less than 10 or 1 if the sensor returns an error condition.

Which of the following logical operator statements is correct

  1. If and only if both of its operands are true or false, logical AND returns true.
  2. If either or both of its operands are true, logical OR returns true.
  3. In C#, logical OR is represented by &&.
  4. In C#, logical NOT is represented by the symbol |.
  5. none of the previous

Java statements using all three logical operators

Operators are the fundamental building blocks of all programming languages. Java, too, has a variety of operators that can be used to accomplish various calculations and functions, whether logical, arithmetic, relational, or otherwise. 

They’re categorized based on the features they offer. Here are several examples-

  1. Arithmetic Operators
  2. Unary Operators
  3. Ternary Operator
  4. Relational Operators
  5. Assignment Operator
  6. Logical Operators
  7. Bitwise Operators
  8. Shift Operators

In Java, there are three types of logical or conditional operators: && (Logical-AND), || (Logical-OR), and! (Logical NOT). The binary logical operators && (Logical-AND) and || (Logical-OR) function on two operands or expressions in this case, whereas, because they return a boolean value, these operators are sometimes referred to as Boolean operators in Java.

      There are three types of logical operators in Java. The table below contains a list of them.

          Operators

          Meaning

&&

AND Operator

||

OR Operator

!

NOT Operator



AND Operator in Java

The AND operator is used to combine two expressions (conditions). The && operator is used to combine two expressions (conditions). The operator returns true if both requirements are met. If either one or both of the expressions are false, the operator returns false.

Eg: if(x>y && y < z)

System.out.println(“Hello java”);

There are two requirements in the preceding statement: x > y and y > z. Because the && operator connects both conditions. “Hello Java” will be displayed if both conditions are met.

OR Operator in Java

The | | (OR) operator combines two or more expressions (conditions) in the OR operator. The operator returns true if either of the conditions is true.

Eg: if(x = 1 || y = 1 || z = 1)

System.out.println(“Hello”);

There are three requirements in the example above: x = 1, y = 1, and z = 1, which are joined by ||. (or operator). The next statement “Hello” will be printed if either x or y or y gets equal to 1. The message will not be displayed if any of the three conditions are not equal to 1.

NOT Operator in Java

The NOT operator is used to revert the operand’s logic state. The logical NOT operator delivers false if the condition is true. The operator returns true if the condition is false.

Eg: if(!(x > y))

System.out.println(“Hello java”);

 If the condition (x > y) is true in the example above, the statement “Hello Java” will not be printed. The statement “Hello Java” will be printed if (x > y) is not true.

Conclusion

Formulas for Mathematical Logic Assemblage (AND) The “AND” operator can be used to connect two statements. A conjunction is another name for it. The symbol for it is “”. If any of the statements in this operator is untrue, the result will be false. If both statements are true, the outcome will also be true. There are two or more inputs but only one output on this device. To conduct logical operations, logical operators are needed. It returns 0 or 1 depending on whether the condition is true or false. In the C programming language, these operators are used to make decisions.

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  • Fehling’s solution
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