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Show that subtraction and division are n...

Show that subtraction and division are not binary operations on N.

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Show that addition, subtraction and multiplication are binary operations on R, but division is not a binary operation on R. Further, show that division is a binary operation on the set R^(**) of nonzero real numbers.

Show that addition and multiplication are associative binary operation on R. But subtraction is not associative on R . Division is not associative on R^(**)

Show that addition and multiplication are associative binary operation on R. But subtraction and division is not associative on R.

Show that -a is the inverse of a for the addition operation '+' on R and 1/a is the inverse of a ne0 for the multiplication operation x on R.

Show that the number of binary operations on {1, 2} having 1 as identity and having 2 as the inverse. of 2 is exactly one.

Determine whether or not each of the definition of ** given below gives a binary operation. In the even that ** is not a binary operation , give justification for this . On Z^(+) , define ** by a" * " b = a - b

Determine whether or not each of the definition of ** given below gives a binary operation. In the even that ** is not a binary operation , give justification for this . On Z^(+) , define ** by a" * " b = ab

Determine whether or not each of the definition of ** given below gives a binary operation. In the even that ** is not a binary operation , give justification for this . On R , define ** by a" * " b = ab^2

KUMAR PRAKASHAN-RELATIONS AND FUNCTIONS -Textbook Illustrations for Practice Work
  1. Let S = {1, 2, 3}. Determine whether the functions f:S rarr S defined ...

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  2. Show that addition, subtraction and multiplication are binary operatio...

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  3. Show that subtraction and division are not binary operations on N.

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  4. Show that ** :Rxx R rarr R given by (a, b) rarr a + 4b^(2) is a bina...

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  5. Let P be the set of all subsets of a given set X. Show that cup: P xxP...

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  6. Show that the VV: RxxR rarr R given by (a, b) rarr max {a, b} and th...

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  7. Show that + : Rxx R rarr R and xx: R xxR rarr R are commutative binar...

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  8. Show that **: RxxR rarr R defined by a^(**) b = a + 2b is not commuta...

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  9. Show that addition and multiplication are associative binary operation...

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  10. Show that ""^** : R xxR rarr R given by a^** b rarr a + 2b is not ass...

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  11. Show that zero is the identity for addition on R and 1 is the identity...

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  12. Show that -a is the inverse of a for the addition operation '+' on R...

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  13. Show that -a is not the inverse of a in N for the addition operation...

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  14. If R1 and R2 are equivalence relations in a set A, show that R(1) cap...

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  15. Let R be a relation on the set A of ordered pairs of positive integers...

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  16. Let X = {1, 2, 3, 4, 5, 6, 7, 8, 9). Let R1 be a relation in X given ...

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  17. Let f: X rarrY be a function. Define a relation R in X given by R = {...

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  18. Determine which of the following binary operations on the set R are as...

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  19. Determine which of the following binary operations on the set R are as...

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  20. Find the number of all one-one functions from set A = {1, 2, 3} to its...

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