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Show that none of the operations given below has identity. (i) `a b = a-b ` (ii) `a b = a^...

200 views · Published 28 September 2017 · 11:05 · Indexed 20 September 2026

Channel: Doubtnut · 2017 · Education

Question From - NCERT Maths Class 12 Chapter 1 EXERCISE 1.4 Question – 10 RELATIONS AND FUNCTIONS CBSE, RBSE, UP, MP, BIHAR BOARD

QUESTION TEXT:-
Show that none of the operations given below has identity. (i) `a ** b = a-b ` (ii) `a ** b = a^2 + b^2 ` (iii) `a ** b = a +ab ` (iv) ` a ** b = (a-b)^2 ` (v) ` a ** b = (ab)/4` (vi) ` a**b = a b^2`

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Related Questions & Solutions:

1. Determine whether or not each of the definition of given below gives a binary operation. In the event that * is not a binary operation, give justification for this. (i) `O n Z^+, d efin e *b ya*b = a ...
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2. For each binary operation * defined below, determine whether * is commutative or associative. (i) `O n Z , d efin e a*b = a - b` (ii) `O n Q , d efin e a*b = a b + 1` (iii) `O n Q , d efin e a*b =(a b...
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3. Consider the binary operation `^^` on the set `{1, 2, 3, 4, 5}` defined by `a^^ b = m in {a , b}` . Write the operation table of the operation `^^` ....
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4. Consider a binary operation * on the set `{1, 2, 3, 4, 5}` given by the following multiplication table. (i) Compute (2*3)*4 a n d 2*(3*4) (ii) I s * com mu t a t i v e ? (iii) Compute (2*3)...
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5. Let `*prime` be the binary operation on the set `{1, 2, 3, 4, 5}` defined by `a*primeb= HdotCdotFdot` of a and b. Is the operation `*prime` same as the operation `*` defined in Exercise 4 above? Justi...
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• NCERT Solutions for Class 12, Chapter 1 - https://doubtnut.com/ncert-solutions/class-12-maths-chapter-1-relations-and-functions-1


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Show that none of the operations given below has identity. (i) `a ** b = a-b ` (ii) `a ** b = a^...

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Show that none of the operations given below has identity. (i) `a b = a-b ` (ii) `a b = a^...