Assignment 1
1
st semester 2016-2017
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Determine whether the statement is true (T) or false (F).
1) The statement “where are you?” is proposition.
2) The conjunction of propositions p and q is denoted by (p ˅ q).
3) The AND function is Boolean multiplication and the OR function is
Boolean addition.
4) The number of Boolean functions of degree 2 is equal to 16.
5) The statement P(x) is said to be the value of the propositional function
P at x.
6) x P(x) asserts P(x) is true for some x in the domain.
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Choose the correct answer
1) The inverse of the statement q →r is
a) ¬ q →r
b) ¬ q →¬r
c) r →q
d) ¬ r →¬q
2) Assume that p ⊕ q is true then
a) Exactly one of p and q must be true
b) Both of p and q must be true
c) No one of p and q must be true
d) Both of p and q must be false
3) Boolean expression for the Boolean function F(x, y) which defined
by the table below is
F( , )
0 0 0
0 1 1
1 0 1
1 1 0
a) ̅ ̅
b) ̅
c) ̅
d) ̅̅ ̅
4) The Boolean expression is equal to
a) X
b) Y
c) 1
d) XY
5) Let Px, y denote "x y 1", the truth values of the quantifications
yxPx, y and xyPx, y are
a) Tand T
b)Tand F
c) F and T
d)F and F
6) The correct translation of the sentence “Some student in this class has
taken a course in Math.” into predicate logic is
a) xMx
b) xMx
c) x ¬ Mx
d) x ¬ Mx
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Solve the following questions
1) Construct a truth table for the proposition
(p → q) ∧ (q → r) → (p → r), then show that it is a tautology.
3) Express the statement “If a person is male and is a parent, then this
person is someone’s Father” as a logical expression involving
predicates, quantifiers where the domain is all people
4) What is the truth value of ∃xP(x), where P(x) is the statement
“ x
3
> 28” and the domain consists of all positive integers not
exceeding 6?
5) Find the sum-of-products expansions of the Boolean
functions F ( , ) = .
6) By using a truth table, Show that x + y = (x ↓ y) ↓ (x ↓ y).