Home
Class 12
MATHS
Determine whether or not each of the def...

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 - b`(ii) `O n Z^+,

Text Solution

Verified by Experts

In `Z^(+), a ** b =a - b`
`2**3 = 2-3 = -1 in Z^(+)`
`therefore` Given operation is not binary.
(ii) In `Z^(+), a ** b = ab`
The product of every two positive intergers is a positive interger.
`therefore` Given operations is binary.
(iii) In R, `a ** b= ab^(2)`
The square of every real number is always a real number.
(iv) In `Z^(+) , " "a**b = a`
The modulus of the difference of every two positive integer.
`therefore` Given operation in binary.
(v) `In Z^(+), " " a**b=a`
For each `a,b in Z^(+)`
`" "a * b = a in Z^(+)`
`therefore` Given operation is binary.
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|19 Videos

  • RELATIONS AND FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 1.3|14 Videos

  • PROBABIILITY

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|19 Videos

  • THREE-DIMENSIONAL GEOMETRY

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|23 Videos

Similar Questions

Explore conceptually related problems

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) On Z^+ , define ∗ by a ∗ b = a – b (ii) On Z^+ , define ∗ by a ∗ b = ab (iii) On R , define ∗ by a ∗ b = ab^2 (iv) On Z^+ , define ∗ by a ∗ b = |a – b| (v) On Z^+ , define ∗ by a ∗ b = a

Determine whether or not the definition of * On Z^+ , defined * by a*b=a b gives a binary operation. In the event that * is not a binary operation give justification of this. Here, Z^+ denotes the set of all non-negative integers.

Determine whether or not the definition of * On Z^+ , defined * by a * b=a-b gives a binary operation. In the event that * is not a binary operation give justification of this. Here, Z^+ denotes the set of all non-negative integers.

Determine whether or not the definition of * On Z^+ , define * by a*b=|a-b| gives a binary operation. In the event that * is not a binary operation give justification of this. Here, Z^+ denotes the set of all non-negative integers.

Determine whether or not the definition of * On Z^+ , define * by a*b=a gives a binary operation. In the event that * is not a binary operation give justification of this. Here, Z^+ denotes the set of all non-negative integers.

Determine whether or not the definition of * On R , define by a*b=a b^2 gives a binary operation. In the event that * is not a binary operation give justification of this. Here, Z^+ denotes the set of all non-negative integers.

Determine whether or not the definition of * On R , define * by a*b=a+4b^2 gives a binary operation. In the event that * is not a binary operation give justification of this. Here, R denotes the set of all real numbers.

Determine whether * on N defined by a*b=a+b-2 for all a ,\ b in N define a binary operation on the given set or not:

Determine whether O on Z defined by a\ O\ b=a^b for all a ,\ b in Z define a binary operation on the given set or not:

Determine whether * on N defined by a*b=a^b for all a ,\ b in N define a binary operation on the given set or not: