Exercise 3.2 Archives - Noon Academy

On the set Z of integers a binary operation * is defined by a 8 b = ab + 1 for all a, b ∈ Z. Prove that * is not associative on Z.

Binary Operations, CBSE, Class 12, Exercise 3.2, Maths, RD Sharma

\[\begin{array}{*{35}{l}} Let\text{ }a,\text{ }b,\text{ }c\text{ }\in \text{ }Z \\ a\text{ }*\text{ }\left( b\text{ }*\text{ }c \right)\text{ }=\text{ }a\text{ }*\text{ }\left( bc\text{ }+\text{ }1...

Show that the binary operation * on Z defined by a * b = 3a + 7b is not commutative?

Binary Operations, CBSE, Class 12, Exercise 3.2, Maths, RD Sharma

\[\begin{array}{*{35}{l}} Let\text{ }a,\text{ }b\text{ }\in \text{ }Z \\ a\text{ }*\text{ }b\text{ }=\text{ }3a\text{ }+\text{ }7b \\ b\text{ }*\text{ }a\text{ }=\text{ }3b\text{ }+\text{ }7a \\...

If the binary operation o is defined by a0b = a + b – ab on the set Q – {-1} of all rational numbers other than 1, show that o is commutative on Q – [1].

Binary Operations, CBSE, Class 12, Exercise 3.2, Maths, RD Sharma

\[\begin{array}{*{35}{l}} Let\text{ }a,\text{ }b\text{ }\in \text{ }Q\text{ }\text{ }-\left\{ -1 \right\}. \\ Then\text{ }aob\text{ }=\text{ }a\text{ }+\text{ }b\text{ }-\text{ }ab \\ =\text{...

Check the commutativity and associativity of each of the following binary operations: (xv) ‘’ on Q defined by a b = gcd (a, b) for all a, b ∈ Q

Binary Operations, CBSE, Class 12, Exercise 3.2, Maths, RD Sharma

(xv) to check: commutativity of * \[\begin{array}{*{35}{l}} Let\text{ }a,\text{ }b\text{ }\in \text{ }N,\text{ }then \\ a\text{ }*\text{ }b\text{ }=\text{ }gcd\text{ }\left( a,\text{ }b \right) ...

Check the commutativity and associativity of each of the following binary operations: (xiii) ‘’ on Q defined by a b = (ab/4) for all a, b ∈ Q (xiv) ‘’ on Z defined by a b = a + b – ab for all a, b ∈ Z

Binary Operations, CBSE, Class 12, Exercise 3.2, Maths, RD Sharma

(xiii) to check :commutativity of * \[\begin{array}{*{35}{l}} Let\text{ }a,\text{ }b\text{ }\in \text{ }Q,\text{ }then \\ a\text{ }*\text{ }b\text{ }=\text{ }\left( ab/4 \right) \\ =\text{ }\left(...

Check the commutativity and associativity of each of the following binary operations: (xi) ‘’ on N defined by a b = ab for all a, b ∈ N (xii) ‘’ on Z defined by a b = a – b for all a, b ∈ Z

Binary Operations, CBSE, Class 12, Exercise 3.2, Maths, RD Sharma

(xi) to check : commutativity of * \[\begin{array}{*{35}{l}} Let\text{ }a,\text{ }b\text{ }\in \text{ }N,\text{ }then \\ a\text{ }*\text{ }b\text{ }=\text{ }{{a}^{b}} \\ b\text{ }*\text{ }a\text{...

Check the commutativity and associativity of each of the following binary operations: (vii) ‘’ on Q defined by a b = a + a b for all a, b ∈ Q (viii) ‘’ on R defined by a b = a + b -7 for all a, b ∈ R

Binary Operations, CBSE, Class 12, Exercise 3.2, Maths, RD Sharma

(vii) to check : commutativity of * \[\begin{array}{*{35}{l}} Let\text{ }a,\text{ }b\text{ }\in \text{ }Q,\text{ }then \\ a\text{ }*\text{ }b\text{ }=\text{ }a\text{ }+\text{ }ab \\ b\text{...

Check the commutativity and associativity of each of the following binary operations: (v) ‘o’ on Q defined by a o b = (ab/2) for all a, b ∈ Q (vi) ‘’ on Q defined by a b = ab2 for all a, b ∈ Q

Binary Operations, CBSE, Class 12, Exercise 3.2, Maths, RD Sharma

(v) to check: commutativity of o \[\begin{array}{*{35}{l}} Let\text{ }a,\text{ }b\text{ }\in \text{ }Q,\text{ }then \\ a\text{ }o\text{ }b\text{ }=\text{ }\left( ab/2 \right) \\ =\text{ }\left(...

Check the commutativity and associativity of each of the following binary operations: (iii) ‘’ on Q defined by a b = a – b for all a, b ∈ Q (iv) ‘⊙’ on Q defined by a ⊙ b = a2 + b2 for all a, b ∈ Q

Binary Operations, CBSE, Class 12, Exercise 3.2, Maths, RD Sharma

(iii) to check: commutativity of * \[\begin{array}{*{35}{l}} Let\text{ }a,\text{ }b\text{ }\in \text{ }Q,\text{ }then \\ a\text{ }*\text{ }b\text{ }=\text{ }a\text{ }-\text{ }b \\ b\text{...

Check the commutativity and associativity of each of the following binary operations: (i) ‘’ on Z defined by a b = a + b + a b for all a, b ∈ Z (ii) ‘’ on N defined by a b = 2ab for all a, b ∈ N

Binary Operations, CBSE, Class 12, Exercise 3.2, Maths, RD Sharma

(i) to check: commutativity of * \[\begin{array}{*{35}{l}} Let\text{ }a,\text{ }b\text{ }\in \text{ }Z \\ =>\text{ }a\text{ }*\text{ }b\text{ }=\text{ }a\text{ }+\text{ }b\text{ }+\text{ }ab ...

Let A be any set containing more than one element. Let ‘’ be a binary operation on A defined by a b = b for all a, b ∈ A Is ‘*’ commutative or associative on A?

Binary Operations, CBSE, Class 12, Exercise 3.2, Maths, RD Sharma

\[\begin{array}{*{35}{l}} Let\text{ }a,\text{ }b\text{ }\in \text{ }A \\ =>\text{ }a\text{ }*\text{ }b\text{ }=\text{ }b \\ b\text{ }*\text{ }a\text{ }=\text{ }a \\ Therefore\text{ }a\text{...

Determine which of the following binary operation is associative and which is commutative: (i) * on N defined by a * b = 1 for all a, b ∈ N (ii) * on Q defined by a * b = (a + b)/2 for all a, b ∈ Q

Binary Operations, CBSE, Class 12, Exercise 3.2, Maths, RD Sharma

(i) to prove: commutativity of * Let \[\begin{array}{*{35}{l}} a,\text{ }b\text{ }\in \text{ }N \\ a\text{ }*\text{ }b\text{ }=\text{ }1 \\ b\text{ }*\text{ }a\text{ }=\text{ }1 \\ =>a\text{...

Let ‘’ be a binary operation on N defined by a b = l.c.m. (a, b) for all a, b ∈ N (i) Find 2 * 4, 3 * 5, 1 * 6. (ii) Check the commutativity and associativity of ‘*’ on N.

Binary Operations, CBSE, Class 12, Exercise 3.2, Maths, RD Sharma

(i) Since, \[\begin{array}{*{35}{l}} a\text{ }*\text{ }b\text{ }=\text{ }1.c.m.\text{ }\left( a,\text{ }b \right) \\ 2\text{ }*\text{ }4\text{ }=\text{ }l.c.m.\text{ }\left( 2,\text{ }4 \right) \\...

On the set Z of integers a binary operation * is defined by a 8 b = ab + 1 for all a, b ∈ Z. Prove that * is not associative on Z.

Show that the binary operation * on Z defined by a * b = 3a + 7b is not commutative?

If the binary operation o is defined by a0b = a + b – ab on the set Q – {-1} of all rational numbers other than 1, show that o is commutative on Q – [1].

Check the commutativity and associativity of each of the following binary operations: (xv) ‘’ on Q defined by a b = gcd (a, b) for all a, b ∈ Q

Check the commutativity and associativity of each of the following binary operations: (xiii) ‘’ on Q defined by a b = (ab/4) for all a, b ∈ Q (xiv) ‘’ on Z defined by a b = a + b – ab for all a, b ∈ Z

Check the commutativity and associativity of each of the following binary operations: (xi) ‘’ on N defined by a b = ab for all a, b ∈ N (xii) ‘’ on Z defined by a b = a – b for all a, b ∈ Z

Check the commutativity and associativity of each of the following binary operations: (vii) ‘’ on Q defined by a b = a + a b for all a, b ∈ Q (viii) ‘’ on R defined by a b = a + b -7 for all a, b ∈ R

Check the commutativity and associativity of each of the following binary operations: (v) ‘o’ on Q defined by a o b = (ab/2) for all a, b ∈ Q (vi) ‘’ on Q defined by a b = ab2 for all a, b ∈ Q

Check the commutativity and associativity of each of the following binary operations: (iii) ‘’ on Q defined by a b = a – b for all a, b ∈ Q (iv) ‘⊙’ on Q defined by a ⊙ b = a2 + b2 for all a, b ∈ Q

Check the commutativity and associativity of each of the following binary operations: (i) ‘’ on Z defined by a b = a + b + a b for all a, b ∈ Z (ii) ‘’ on N defined by a b = 2ab for all a, b ∈ N

Let A be any set containing more than one element. Let ‘’ be a binary operation on A defined by a b = b for all a, b ∈ A Is ‘*’ commutative or associative on A?

Determine which of the following binary operation is associative and which is commutative: (i) * on N defined by a * b = 1 for all a, b ∈ N (ii) * on Q defined by a * b = (a + b)/2 for all a, b ∈ Q

Let ‘’ be a binary operation on N defined by a b = l.c.m. (a, b) for all a, b ∈ N (i) Find 2 * 4, 3 * 5, 1 * 6. (ii) Check the commutativity and associativity of ‘*’ on N.

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