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True or False statements : The binary ...

True or False statements :
The binary operation * defined in Z by a * b = a + b is commutative but not associative.

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Let '*' be the binary operation defined on R by a*b = 1 + ab AA a,binR Commutative but not associative.

Let '*' be the binary operation defined on R by a*b = 1 + ab AA a,binR neither commutative nor associative.

Let '*' be the binary operation defined on R by a*b = 1 + ab AA a,binR both commutative and associative.

Let '*' be the binary operation defined on R by a*b = 1 + ab AA a,binR associative butnot commutative.

Show that the binary operation on the set 'N' given by a * b =1 AA a,b in N is commutative as well as associative.

Let ∗ be the binary operation on N defined by a*b=H.C.F. of a and b . Is ∗ commutative?

PRADEEP PUBLICATION-RELATIONS AND FUNCTIONS-EXERCISE
  1. True or False statements : The function f : R rarr R defined by f(x)...

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  2. Let A = {0, 1} and N be the set of natural numbers. Then the mapping f...

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  3. True or False statements : The binary operation * defined in Z by a ...

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  4. An integer m is said to be related to another integer n if m is a inte...

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  5. Let R be a relation from a set A to a set B, then:

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  6. True or False statements : Composition of functions is associative.

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  7. True or False statements : The function f : R rarr R defined by f(x)...

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  8. Let f : A rarr B and g : B rarr C be onto functions, show that gof is ...

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  9. Let f : A rarr B and g : B rarr C be onto functions, show that gof is ...

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  10. For all sets A, B and C, if A⊂ C and B ⊂ C,then A∪ B ⊂ C.

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  11. Match the following : .

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  12. Consider the set A = (a,b). The smallest equivalence relation that can...

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  13. Consider the set A = (1,2). Which of the following relations on A is s...

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  14. Let A be a finite set containing n distinct elements. The number of re...

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  15. Let T be the set of all triangles in the Euclidean plane, and let a re...

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  16. Consider the non-empty set consisting of children in a family and a re...

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  17. If a relation R on the set {1, 2, 3} be defined by R = {(1, 2)}, then ...

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  18. Let R be a relation defined by R = {(a, b) : a ge b}, where a and b a...

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  19. Let R be the relation defined on the set N of natural numbers by the r...

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  20. Let A = (a,b,c) and R = (a,a), (b,b), (c,c), (b,c), (a,b) be a relatio...

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