Math 1 Assignment

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1.) Write the given statement in the “if…then” form:

“All mathematicians are ogres.”

Answer:

If a person is a mathematician, then the person is an ogre.

“All counting numbers are divisible by 3.”

Answer:

If the number is a counting number (1, 2, 3, 4…. +∞), then it would be divisible by 3.

2.) Let p: price will rise; q: taxes will rise

Translate the ff into words:

a.) p v q b.) ~p^q c.) ~pv~q

Answers:

a.) P v Q means the conjunction of p and q. The whole statement would say: “The Price will rise and the taxes will rise”.

b.) ~P ^ Q is the disjunction of not of P and Q. The whole statement would then say: “The price will not rise or taxes will rise”.

c.) ~P V ~Q is the conjunction of not of P and not of Q. The whole statement would then say: “The price will not rise and taxes will not rise”.

d.)

3.) Write the contrapositive of the ff. statement:

“If you break the law, then you will go to jail.”

Answer:

“If you not break the law, then you will not go to jail.”

4.) Let p: 5+10 = 16 ; q= 15-10 = 3

a.) Give the truth value of p~q.

Answer

p: 5+10 = 16 is false.

q: 15-10 = 3 is also false.

Therefore p~q is

p is false

~q is true (not of false is true).

b.) Is the ff statement true or false? “If 5+10 = 6 then 15-10=3”

If false (5+10 is not 6) then false (15-10 is not 3) would be true. A false hypothesis coupled with a false conclusion results in a true statement.

5.) Is the ff. statement true or false ?

a.) p: 2 is prime

2 is a prime so it is true.

b.) q: 1 is prime

1 is not a prime so its false.

c.) (p^q) v (~q)

(true and false) or (~false)

True and false is false so (true and false) is false. Not of false is true so (~false) becomes true. The whole statement would then turn into false or true which is true. The whole statement is true.

6.) Use truth tables to decide whether the argument is valid or not

P Q (~q) (p^q) (p^q) v (~q)

True False True False True

7.) Use Euler diagrams to decide whether an argument is valid or not.

Euler diagrams are same not really the same with venn diagram as III – 3 would be

V. Numeration System:

Each group must submit 5 questions (w/ solutions), to include in the exam

VI. GCF, LCM, Prime Factorization

VII. Modular Systems

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