المشاركة الأصلية كتبت بواسطة khaliid

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المشاركة الأصلية كتبت بواسطة joory248

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 px, y denote "x  y  1", the truth values of the quantifications
yxpx, y and xypx, 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) xmx
b) xmx
c) x ¬ mx
d) x ¬ mx

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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).