Binary operations

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Binary operations

In Class 12 Mathematics, this topic introduces binary operations as functions that combine two elements of a set to produce another element of the same set. Within the chapter Relations and Functions, students learn to identify whether an operation is well-defined and closed, represent it through tables or algebraic rules, and examine key properties such as commutativity, associativity, identity elements, and inverses. Examples involving familiar number systems help connect these ideas with broader function concepts.

Quiz this set

On (\mathbb{R}), (a*b=a+b-3). What is the inverse of (8)?

On (\mathbb{R}), (ab=a+b-3). What is the value of ((25)*7)?

On (\mathbb{R}), (ab=a+b-3). What is the simplified form of (a(b*c))?

If (a*b=a+b+\lambda ab) and (\lambda\neq0), what is the identity element?

On (\mathbb{R}), (a*b=a+b+\lambda ab). Under which condition will the inverse of (a) exist?

In (a*b=a+b+\lambda ab) on (\mathbb{R}), (\lambda=2). What is the inverse of (4)?

On (A={1,2,4,8}), (a*b=\operatorname{lcm}(a,b)). Which statement is correct?

On (\mathbb{Z}), the operation (a*b=a+b+ab) is defined. Choose the correct statement.

On (\mathbb{R}), the operation (a*b=a+b+4) is defined. What is its identity element?

On (\mathbb{R}), (a*b=a+b+4). What is the inverse of (6)?

On (\mathbb{R}), (a*b=a+b-ab). Which is its identity element?

On (\mathbb{R}), (a*b=a+b-ab). What is the inverse of (4)?

On (A=\mathbb{R}-{-1}), (a*b=a+b+ab). What is the identity element?

On (A=\mathbb{R}-{-1}), (a*b=a+b+ab). What is the inverse of (2)?

On (\mathbb{R}), (a*b=a+b+ab). Which number does not have an inverse?

On (\mathbb{Q}-{0}), (a*b=\frac{ab}{5}). Which is the identity element?

On (\mathbb{Q}-{0}), (a*b=\frac{ab}{5}). What is the inverse of (10)?

On (A={2,4,6,8}), (a*b=\max(a,b)). What is its identity element?

On (A={2,4,6,8}), (a*b=\min(a,b)). Which is the identity element?

On (A={1,2,3,6}), (a*b=\gcd(a,b)). What is the identity element of this operation?

On (A={1,2,3,6}), (a*b=\operatorname{lcm}(a,b)). What will be the identity element?

On (\mathbb{Z}), (a*b=a-b). Which statement is correct?

On (\mathbb{Z}), (a*b=\frac{a+b}{2}) is defined. Why is it not a binary operation?

On (\mathbb{R}), (a*b=a^2+b^2). Choose the correct property.

If (a*b=ka+b) on (\mathbb{R}) is commutative, what is the value of (k)?

Quiz result

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Binary operations

Quiz this set

On (\mathbb{R}), (a*b=a+b-3). What is the inverse of (8)?(\mathbb{R}) पर (a*b=a+b-3) है। (8) का प्रतिलोम क्या है?

On (\mathbb{R}), (a*b=a+b-3). What is the value of ((2*5)*7)?(\mathbb{R}) पर (a*b=a+b-3) है। ((2*5)*7) का मान क्या है?

On (\mathbb{R}), (a*b=a+b-3). What is the simplified form of (a*(b*c))?(\mathbb{R}) पर (a*b=a+b-3) है। (a*(b*c)) का सरल रूप क्या है?

If (a*b=a+b+\lambda ab) and (\lambda\neq0), what is the identity element?यदि (a*b=a+b+\lambda ab) और (\lambda\neq0), तो तत्समक अवयव क्या है?

On (\mathbb{R}), (a*b=a+b+\lambda ab). Under which condition will the inverse of (a) exist?(\mathbb{R}) पर (a*b=a+b+\lambda ab) है। किस शर्त पर (a) का प्रतिलोम मौजूद होगा?

In (a*b=a+b+\lambda ab) on (\mathbb{R}), (\lambda=2). What is the inverse of (4)?(\mathbb{R}) पर (a*b=a+b+\lambda ab) में (\lambda=2) है। (4) का प्रतिलोम क्या है?

On (A={1,2,4,8}), (a*b=\operatorname{lcm}(a,b)). Which statement is correct?समुच्चय (A={1,2,4,8}) पर (a*b=\operatorname{lcm}(a,b)) है। कौन-सा कथन सही है?

On (\mathbb{Z}), the operation (a*b=a+b+ab) is defined. Choose the correct statement.समुच्चय (\mathbb{Z}) पर संक्रिया (a*b=a+b+ab) दी है। सही कथन चुनिए।

On (\mathbb{R}), the operation (a*b=a+b+4) is defined. What is its identity element?समुच्चय (\mathbb{R}) पर संक्रिया (a*b=a+b+4) है। इसका तत्समक अवयव क्या है?

On (\mathbb{R}), (a*b=a+b+4). What is the inverse of (6)?समुच्चय (\mathbb{R}) पर (a*b=a+b+4) है। (6) का प्रतिलोम क्या होगा?

On (\mathbb{R}), (a*b=a+b-ab). Which is its identity element?समुच्चय (\mathbb{R}) पर (a*b=a+b-ab) है। इसका तत्समक अवयव कौन-सा है?

On (\mathbb{R}), (a*b=a+b-ab). What is the inverse of (4)?समुच्चय (\mathbb{R}) पर (a*b=a+b-ab) है। (4) का प्रतिलोम क्या है?

On (A=\mathbb{R}-{-1}), (a*b=a+b+ab). What is the identity element?समुच्चय (A=\mathbb{R}-{-1}) पर (a*b=a+b+ab) है। तत्समक अवयव क्या है?

On (A=\mathbb{R}-{-1}), (a*b=a+b+ab). What is the inverse of (2)?समुच्चय (A=\mathbb{R}-{-1}) पर (a*b=a+b+ab) है। (2) का प्रतिलोम क्या होगा?

On (\mathbb{R}), (a*b=a+b+ab). Which number does not have an inverse?समुच्चय (\mathbb{R}) पर (a*b=a+b+ab) है। किस संख्या का प्रतिलोम नहीं बनता?

On (\mathbb{Q}-{0}), (a*b=\frac{ab}{5}). Which is the identity element?समुच्चय (\mathbb{Q}-{0}) पर (a*b=\frac{ab}{5}) है। तत्समक अवयव कौन-सा है?

On (\mathbb{Q}-{0}), (a*b=\frac{ab}{5}). What is the inverse of (10)?समुच्चय (\mathbb{Q}-{0}) पर (a*b=\frac{ab}{5}) है। (10) का प्रतिलोम क्या होगा?

On (A={2,4,6,8}), (a*b=\max(a,b)). What is its identity element?समुच्चय (A={2,4,6,8}) पर (a*b=\max(a,b)) है। इसका तत्समक अवयव क्या है?

On (A={2,4,6,8}), (a*b=\min(a,b)). Which is the identity element?समुच्चय (A={2,4,6,8}) पर (a*b=\min(a,b)) है। तत्समक अवयव कौन-सा है?

On (A={1,2,3,6}), (a*b=\gcd(a,b)). What is the identity element of this operation?समुच्चय (A={1,2,3,6}) पर (a*b=\gcd(a,b)) है। इस संक्रिया का तत्समक अवयव क्या है?

On (A={1,2,3,6}), (a*b=\operatorname{lcm}(a,b)). What will be the identity element?समुच्चय (A={1,2,3,6}) पर (a*b=\operatorname{lcm}(a,b)) है। तत्समक अवयव क्या होगा?

On (\mathbb{Z}), (a*b=a-b). Which statement is correct?समुच्चय (\mathbb{Z}) पर (a*b=a-b) है। कौन-सा कथन सही है?

On (\mathbb{Z}), (a*b=\frac{a+b}{2}) is defined. Why is it not a binary operation?समुच्चय (\mathbb{Z}) पर (a*b=\frac{a+b}{2}) दिया है। यह द्विआधारी संक्रिया क्यों नहीं है?

On (\mathbb{R}), (a*b=a^2+b^2). Choose the correct property.समुच्चय (\mathbb{R}) पर (a*b=a^2+b^2) है। सही गुण चुनिए।

If (a*b=ka+b) on (\mathbb{R}) is commutative, what is the value of (k)?यदि (\mathbb{R}) पर (a*b=ka+b) क्रमविनिमेय है, तो (k) का मान क्या होगा?

Quiz result

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On (\mathbb{R}), (a*b=a+b-3). What is the inverse of (8)?

On (\mathbb{R}), (ab=a+b-3). What is the value of ((25)*7)?

On (\mathbb{R}), (ab=a+b-3). What is the simplified form of (a(b*c))?

If (a*b=a+b+\lambda ab) and (\lambda\neq0), what is the identity element?

On (\mathbb{R}), (a*b=a+b+\lambda ab). Under which condition will the inverse of (a) exist?

In (a*b=a+b+\lambda ab) on (\mathbb{R}), (\lambda=2). What is the inverse of (4)?

On (A={1,2,4,8}), (a*b=\operatorname{lcm}(a,b)). Which statement is correct?

On (\mathbb{Z}), the operation (a*b=a+b+ab) is defined. Choose the correct statement.

On (\mathbb{R}), the operation (a*b=a+b+4) is defined. What is its identity element?

On (\mathbb{R}), (a*b=a+b+4). What is the inverse of (6)?

On (\mathbb{R}), (a*b=a+b-ab). Which is its identity element?

On (\mathbb{R}), (a*b=a+b-ab). What is the inverse of (4)?

On (A=\mathbb{R}-{-1}), (a*b=a+b+ab). What is the identity element?

On (A=\mathbb{R}-{-1}), (a*b=a+b+ab). What is the inverse of (2)?

On (\mathbb{R}), (a*b=a+b+ab). Which number does not have an inverse?

On (\mathbb{Q}-{0}), (a*b=\frac{ab}{5}). Which is the identity element?

On (\mathbb{Q}-{0}), (a*b=\frac{ab}{5}). What is the inverse of (10)?

On (A={2,4,6,8}), (a*b=\max(a,b)). What is its identity element?

On (A={2,4,6,8}), (a*b=\min(a,b)). Which is the identity element?

On (A={1,2,3,6}), (a*b=\gcd(a,b)). What is the identity element of this operation?

On (A={1,2,3,6}), (a*b=\operatorname{lcm}(a,b)). What will be the identity element?

On (\mathbb{Z}), (a*b=a-b). Which statement is correct?

On (\mathbb{Z}), (a*b=\frac{a+b}{2}) is defined. Why is it not a binary operation?

On (\mathbb{R}), (a*b=a^2+b^2). Choose the correct property.

If (a*b=ka+b) on (\mathbb{R}) is commutative, what is the value of (k)?