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Give a relation which is both a partially ordered relation and an equivalence relation on a set.
Show that if eight people are in a room, at least two of them have birthdays that occur on the same day of the week.
Consider f; Z+ → Z+ define by f(a) =a2. Check if f is one-to-one and / or into using suitable explanation
Let X = {a, b, c} defined by f : X ®X such that f = {(a, b), (b, a), (c,c)}. Find the values of
f–1, f2 and f4
(Assume that r=a/h is a root, where a and b are integers and a/b is in lowest terms.obtain an equation involving integers by multiplying by then look at whether a and bare each odd or
even.
Q#: A binary operation ∇ on [0,1] is a t-norm if and only if x∇(y∇z)=(x∇y)∇z
f (x) = (x2 + 1)/(x2 + 2)
Create the equivalent logic circuit of the following logic expression:
1. Q = (A + B) . (C +D)'
2. F1 = (A + BC') . D
3. Q = [(A + B)' . C] +B . C
Find the complement of the following expression using dual of a function:
1. xy' + x'y
2. (AB' + C) D' + E
3. AB (C'D + CD') + A'B' (C' +D) (C + D')
4. (x + y+ z) (x' + z') (x + y)
Boolean expressions to minimal number of literals:
1. x'y' + xy + x'y
2. (x + y) (x + y')
3. x'y + xy' + xy + x'y'
4. x' + xy +xz' + xy'z'
5. A'C' + ABC + AC'
6. (x'y' + z)' + z + xy + wz
7. A'B (D' + C'D) + B (A + A'CD)
