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## Short Assignment Requirements

Textbook:Rosen, K.H. (2012). Discrete Mathematics and its Applications (7th ed.). New York, NY: McGraw Hill. ISBN: 978-0077431440 (print version).

## Assignment Description

Ministry of Higher EducationCSTS

Kingdom of Saudi ArabiaSEU, KSA

Discrete Mathematics (Math 150)

Level III, Assignment 1 (2017)

1.    State whether the following statements are true or false:     [6]

(a)     12+4=7-16 is a proposition.

(a)

(b)    The AND operation of two propositions p and q denoted by p q is true if both propositions are not true.

(b)                   (c) In Boolean algebra, x¯¯ = ¯x.

(c)                    (d) Boolean algebra simplifies logic circuits.

(d)

(e)    The nested quantifier with real numbers x, y, ∃xyP(x,y), where P(x,y) : x + y = 0, is true.

(e)

(f)     If Q(x,y) : x + y = x y with domain consists of all integers, then ∃xQ(x,2) is

False.

(f)

Due Date: 22.10.2017

Math 150                                                                                            Department of Mathematics

2.    Select one of the alternatives from the following questions as your answer.          [6]

(a)     The inverse of the proposition q p is

A.      ¬p →¬q B. p q

C. ¬q →¬p D. p →¬q

(b)    The symbolization for a conjunction of two propositions p and q is

A.      p q

B.      p q

C.      p q

D.     p q

(c)     A boolean function may be transformed into a A. logical expression.

B.      map.

C.      matrix.

D.     none of the above.

(d)    The degree of the Boolean function given by f(x,y,z,w) = xy + yz + zw is

A.      2

B.      4

C.      3

D.     1

(e)     Translate ∀xy(x < y) in English, considering domain as real number for both the variable.

A.      For every real number y there exists a real number x such that x is less than y.

B.      For some real number x there exists a real number y such that x is less than y.

C.      For all real number x there exists a real number y such that x is less than y.

D.     For each and every real number x and y such that x is less than y. Due Date: 22.10.2017

Math 150                                                                                            Department of Mathematics

(f)      Express, The difference of a real number and itself is zero using required operators.

A.      x(x x! = 0)

B.      xy(x y = 0) C. ∃x(x x = 0)

D. ∀x(x x = 0)

 3. Construct the truth table for the compound proposition(p ∧ q) ∨ (¬p ∨¬q). [3] 4. Show that the conditional statement (p ∧ q) → (p → q) is a tautology. [3] 5. Use a table to express the values of the boolean function given byf(x,y) = xy¯+ ¯xy. [3] 6. Construct a combinatorial circuit using inverter, OR gates and AND gates that produces the output ¯pq¯+ pq, from input bits p and q. [3] 7. Express the following sentences in predicate quantifiers notations:(a)     Every comedian is funny.(b)    There is a comedian who is not funny. [3] 8. Use predicate quantifiers, logical connectives and mathematical operators to express the statement that the average of two positive real numbers is always positive. [3]

End of Assignment.

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