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Commutative & Associative Properties: Binary Operations Video Lecture | Mathematics (Maths) for JEE Main & Advanced

209 videos|443 docs|143 tests

FAQs on Commutative & Associative Properties: Binary Operations Video Lecture - Mathematics (Maths) for JEE Main & Advanced

1. What is the commutative property of binary operations?
Ans. The commutative property states that for any binary operation, changing the order of the operands does not change the result. In other words, if a and b are two elements, the commutative property states that a * b = b * a.
2. Can you give an example of the commutative property in action?
Ans. Yes, for example, the commutative property is applicable to addition and multiplication. For addition, 2 + 3 is equal to 3 + 2, and for multiplication, 4 * 5 is equal to 5 * 4. In both cases, changing the order of the operands does not affect the result.
3. What is the associative property of binary operations?
Ans. The associative property states that for any binary operation, the grouping of the operands does not affect the result. In other words, if a, b, and c are three elements, the associative property states that (a * b) * c = a * (b * c).
4. Can you provide an example of the associative property in action?
Ans. Certainly! The associative property is applicable to addition and multiplication as well. For addition, (2 + 3) + 4 is equal to 2 + (3 + 4), and for multiplication, (4 * 5) * 6 is equal to 4 * (5 * 6). In both cases, changing the grouping of the operands does not change the result.
5. How are the commutative and associative properties different?
Ans. The commutative property deals with changing the order of operands in a binary operation, while the associative property deals with changing the grouping of the operands. In simple terms, the commutative property focuses on switching the positions of elements, while the associative property focuses on rearranging the parentheses or brackets used in expressions. Both properties ensure that the result remains the same regardless of the order or grouping used.
209 videos|443 docs|143 tests

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