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Let L be the set of all lines in a plane...

Let L be the set of all lines in a plane and R be the relation in L defined as `R = {(L _(1), L _(2)) : L _(1)` is perpendicular to `L _(2)` }. Show that R is symmetric but neither reflexive nor transitive.

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KUMAR PRAKASHAN-RELATIONS AND FUNCTIONS -Textbook Illustrations for Practice Work
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  2. Let T be the set of all triangles in a plane with R a relation in T g...

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  3. Let L be the set of all lines in a plane and R be the relation in L de...

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  4. Show that the relation R in the set {1,2,3} given by R = {(1,1) ,(2,2)...

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  5. Show that the relation R in the set Z of intergers given by R ={(a,...

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  6. Let R be the realtion defined in the set A = {1,2,3,4,5,6,7} by R ={(a...

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  7. Let A be the set of all 50 students of Class X in a school. Let f : A ...

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  8. Show that the function f:N rarr N , given by f(x) = 2x, is one-one but...

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  9. Prove that the function f :R rarr R , given by f(x) = 2x, is one-one a...

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  10. Show that the function f:N rarr N , given by f(1) = f(2) = 1 and f(x) ...

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  11. Show that the function f: R rarr R , defined as f(x) = x^2 , is neithe...

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  12. Show that f:N rarr N , given by f(x) = {:{(x+1, " if x is odd"),(x-1...

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  13. Show that an onto function f : {1, 2, 3} rarr {1, 2, 3} is always one...

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  14. Show that a one-one function f : {1, 2, 3} rarr {1, 2, 3} must be ont...

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  15. Let f: {2, 3, 4, 5} rarr {3, 4, 5, 9} and g : {3, 4, 5, 9} rarr {7, 1...

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  16. Find gof and fog, if f:R rarr R and g: R rarrR are given by f(x) = c...

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  17. Show that if f: R - {7/5} rarr R - {3/5} is defined by f(x) = (3x+4)/...

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  18. Show that if f: A rarr B and g: B rarr C are one- one, then gof: A ra...

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  19. Show that if f: A rarr B and g: B rarr C are onto, then gof: A rarr ...

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  20. Consider functions f and g such that composite gof is defined and is o...

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