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# We Helped With This Algebra Homework: Have A Similar One?

Category | Math |
---|---|

Subject | Algebra |

Difficulty | Undergraduate |

Status | Solved |

More Info | Calculus Help |

## Short Assignment Requirements

## 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*, ∃*x*∀*yP*(*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
∀*x*∃*y*(*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. ∀*x*∀*y*(*x *− *y *= 0) C. ∃*x*(*x *− *x *= 0)

D. ∀*x*(*x *− *x *= 0)

3. Construct the truth table for the compound proposition ( | [3] |

4.
Show that the conditional statement ( | [3] |

5. Use a table to express the values of the boolean function given by
| [3] |

6. Construct a combinatorial circuit
using inverter, OR gates and AND gates that produces the output ¯ | [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.