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Determine whether ** is a binary operati...

Determine whether `**` is a binary operation on the sets given below.
(i) `a ** b=a.|b|` on R.
(ii) `a ** b`= min (a,b) on A={1,2,3,4,5}
(iii) `(a ** b) = asqrt(b)` is binary on R.

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PREMIERS PUBLISHERS-DISCRETE MATHEMATICS-Solution To Exercise 12.1
  1. Determine whether ** is a binary operation on the sets given below. ...

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  2. Determine whether ** is a binary operation on the sets given below. ...

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  3. On Z, define ox by (m ox n) = m^(n) + n^(m) : AA m, n in Z. Is ox bina...

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  4. Let ** be defined on R by (a ** b) = a+b + ab -7. Is ** binary on R? I...

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  5. Let A={a + sqrt(5)b: a, b in Z}. Check whether the usual multiplicatio...

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  6. Define an operation * on Q as follows: a * b =((a+b)/(2)), a, b in Q. ...

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  7. Define an operation * on Q as follows: a * b =((a+b)/(2)), a, b in Q. ...

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  8. Fill in the following table so that the binary operation ** on A={a,b,...

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  9. Consider the binary operation * defined on the set A= {a,b,c,d} by the...

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  10. Let A =({:(1,0,1,0),(0,1,0,1),(1,0,0,1):}), B=({:(0,1,0,1),(1,0,1,0),(...

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  11. Let A =({:(1,0,1,0),(0,1,0,1),(1,0,0,1):}), B=({:(0,1,0,1),(1,0,1,0),(...

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  12. Let A =({:(1,0,1,0),(0,1,0,1),(1,0,0,1):}), B=({:(0,1,0,1),(1,0,1,0),(...

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  13. Let A =({:(1,0,1,0),(0,1,0,1),(1,0,0,1):}), B=({:(0,1,0,1),(1,0,1,0),(...

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  14. Let M={[{:(,x,x),(,x,x):}}: x in R-{0}} and let * be the matrix multip...

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  15. Let M={[{:(,x,x),(,x,x):}}: x in R-{0}} and let * be the matrix multip...

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  16. Let A be Q/{1}. Define * on A by x * y=x+y-xy. Is * binary on A? If so...

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  17. Let A be Q/{1}. Define * on A by x * y=x+y-xy. Is * binary on A? If so...

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