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Worksheets

Logic

Total questions: 27

Worksheet time: 15mins

Name
Class
Date
1.

If the class wins the game, then the teacher will give bonus points


When will this implication become a false statement

a)

p: True , q: True

b)

p: True , q: False

c)

p : False, q : False

d)

p : False, q : True

2.

I will be alive if and only if I will be breathing


This equivalence(iff) statement will be false when....


Hint: Write a truth table to help you

a)

p: True , q: True

b)

p : False, q : False

c)

p : True , q : False

d)

p : False, q: True

3.

If i miss the bus, then I will walk to school


State the antecedent in this implication

a)

I miss the bus

b)

I will walk to school

c)

Ya'll get a tardy

d)

I dont walk to school

4.

If I dont come to Monday/Tuesday afterschool to retake the functions quiz, then I will miss a great opportunity


Which is the consequent in this implication?

a)

If I dont come to Monday/Tuesday afterschool to retake the functions quiz

b)

Functions quiz is a good opportunity to prepare for the Quarter Exam on Friday too

c)

Also dont forget your pizza/pie for Pi day (13/3)

d)

I will miss a great opportunity

5.

Write down the implicative statement

p -> q


p : There are eggs in the fridge

q: Nice will bake a cake

a)

There are eggs in the fridge if and only if Nice will bake a cake

b)

If there are no eggs in the fridge, then Nice will not bake a cake

c)

If Nice bakes an egg, then there is cake in the fridge

d)

If there are eggs in the fridge then Nice will bake a cake

6.

p: Cows have nine legs

q: Horses have 5 heads


Write down the equivalence of statement AND state whether the equivalence is True/False

a)

If cows have nine legs then horses have 5 heads, True

b)

Cows have nine legs if and only if Horses have 5 heads, False

c)

If cows have nine legs then horses have 5 heads, False

d)

Cows have nine legs if and only if Horses have 5 heads, True

7.

Construct the following truth table


p → ¬ q


Everyone must have it to receive code

a)

Monkeys

b)

Spiders

c)

Rams

d)

Horses

8.

Construct the following truth table


q Λ (p → q)


Everyone must have the table to receive the code...

a)

Jelly Beans

b)

Cheeseburger

c)

Green Tea

d)

Popcorn

9.

Write a truth table for the following...


(p ↔ q) Λ ¬ p

a)

Pepsi

b)

Ice Tea

c)

Sprite

d)

Red Bull

10.

Write the converse of the statement


p: If i have 20 baht

q: I will buy "PopPop"

a)

If I have 20 baht, then I will buy PopPop

b)

If I have PopPop, then I have 20 baht

c)

If i dont have PopPop, then I dont have 20 baht

d)

If i dont have 20 baht, then I will not buy PopPop

11.

Write the Inverse of the statement


If Its cold, then I will wear a jacket

a)

If I wear a jacket, then its cold

b)

If I dont wear a jacket, then its not cold

c)

If its not cold, then I will not wear a jacket

d)

If i wear a jacket, then its cold

12.

Write down the contrapositive of the statement


if Jenny gets an "A" on her Math test, then she will achieve her goal

a)

If Jenny does not get an A on her math test, then she will not achieve her goal

b)

If Jenny does not achieve her goal, then she will not get an A on her test

c)

If Jenny achieves her goal, then she will get an A on her Math test

13.

Parallel lines will intersect

a)

Proposition, True

b)

Proposition, False

c)

Proposition, Indeterminate

d)

Not a proposition

14.

A triangle has 3 sides

a)

Proposition, True

b)

Proposition, False

c)

Proposition, Indeterminate

d)

Not a proposition

15.

Sheen loves Math

a)

Proposition, True

b)

Proposition, False

c)

Proposition, Indeterminate

d)

Not a proposition

16.

x is a dog for x ∈ {dogs, cats}


Find negation

a)

x is a cat

b)

x is dogs and cats

c)

x is dogs

17.

This repersents...

a)

The Solar eclipse in progress

b)

Conjunction

c)

Disjunction

d)

Exclusive Disjunction

18.

Determine if the following proposition p V q is true or false


p: The mean of 5 and 9 is 7

q: The mean of 8 and 14 is 10

a)

True

b)

False

c)

Indeterminate

d)

I forgot what mean is

19.

For the following proposition, determine a V b is true or false


a: 4.5 ∈ ℤ

b: -8 ∈ ℕ

a)

True

b)

False

c)

Indeterminate

20.

Are these logically equivalent

a)

Yes

b)

No

c)

Maybe

21.

Perform a truth table for the following

a)

M

b)

U

c)

I

d)

D

e)

S

22.

When f: 2x - 2


Find f-1(6)

a)

2

b)

5

c)

4

d)

-3

23.

What is the range of the function f for the domain -3 < x < 3


f(x) = 5x - 2

a)

-17 < y < 13

b)

-10 < y < 14

c)

-17 < y < 13

d)

-10 < y < 14

24.

What is the image of 7 by the function g


g : x/(x-2)

a)

2/3

b)

4/5

c)

9/4

d)

7/5

25.

Find gf:


When g: x / (x-2) and f: 5x -2

a)

5x-2

b)

5x-2/(5x-4)

c)

5x - 4

d)

2x - 3/ (3x - 4)

26.

Find fg when f : 5x - 2 and g: x/(x-2)

a)

(x-2)/5x

b)

3x + 4/(x-2)

c)

2x - 5

d)

5x -5

27.

Solve the equation


∣(x-3)2 - 4∣ = x - 1

a)

2, 3, 4

b)

1, 6

c)

4, 8

d)

1, 4, 6

e)

1, 3, 6

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