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)
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
Let D70 = {1, 2, 57, 10, 14, 35, 70} Define '+', '·' and '" by a + b = lcm (a, b), a . b = gcd (a, b) and a' = for all a, b D70. The value of (2 + 7)(14 . 10)' is
7
14
35
5
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'
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' = Then (15' + 6) · 10 1s equal to :
1
2
3
5
Let f(x) = ax(a > 0) be written as f(x) = f1(x) + f2(x), where f1(x) is an even function and f2(x) is an odd function. Then f1(x + y) + f1(x – y) equals :
2f1(x)f1(y)
2f1(x + y)f1(x - y)
2f1(x + y)f2(x - y)
2f1(x)f2(y)