Let a be any element in a Boolean Algebra B. If a + x = 1 and ax

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241.

Let S be the set of all real numbers. Then the relation R = {(a, b): 1 + ab > 0} on S is :

  • reflexive and symmetric but not transitive

  • reflexive and transitive but not symmetric

  • symmetric and transitive but not reflexive

  • reflexive, transitive and symmetric


242.

Let fx + 1x = x2 + 1x2, x  0, then f(x) equals to :

  • x2

  • x2 - 1

  • x2 - 2

  • x2 + 1


243.

Let f : R  R : f(x) = x2 and g : R  R : g(x) = x + 5, then gof is :

  • (x + 5)

  • (x + 52)

  • (x2 + 52)

  • (x2 + 5)


244.

The output s as a Boolean expression in the inputs x1, x2 and x3 for the logic circuit in the following figure is

  • x1 x'2 + x'2 + x3

  • x1 + x'2x3 + x3

  • (x1x2)' + x1x'2x3

  • x1x'2 + x'2x3


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245.

Let D70 = {1, 2, 57, 10, 14, 35, 70} Define '+', '·' and '" by a + b = lcm (a, b), a . b = gcd (a, b) and a' = 702 for all a, b  D70. The value of (2 + 7)(14 . 10)' is

  • 7

  • 14

  • 35

  • 5


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246.

Let a be any element in a Boolean Algebra B. If a + x = 1 and ax = 0, then :

  • x = 1

  • x = 0

  • x = a

  • x = a'


D.

x = a'

The given conditions are

a + x = 1

and ax = 0

The above two conditions will be true, if x = a'.


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247.

then s is equal to :

  • x . (y' + z)

  • x . (y' + z')

  • x . (y + z)

  • (x + y) . z


248.

If Na = {an : n  N}, then N5 n N7 is equal to :

  • N7

  • N

  • N35

  • N5


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249.

If fx = αxx + 1, x  - 1, for what value of α is ffx = x ?

  • 2

  • - 2

  • 1

  • - 1


250.

Let D = {1, 2, 35, 6, 10, 15, 30}. Define the operattons '+', ' . ' and ' ' ' on D as follows a + b = LCM(a, b), a . b = GCD(a, b) and a' = 30a Then (15' + 6) · 10 1s equal to :

  • 1

  • 2

  • 3

  • 5


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