Logic statement(D1)

Unit Two Test

Choose:(20’)

1.What would be the next two number in the following set?{7, 9, 11, 13}( ).

A)10, 12 B)13, 14 C)12, 13 D)15, 17 2.What shape and how many of this shape will be next in the pattern below?( ).

A)1 Circle B)3 Circles C)1 Triangle D)3 Triangles 3.Identify the if-then form of the given statement.\ )

A)If a polygon is regular, then it has all its sides equal. B)A polygon is regular, if it has all its sides equal. C)A regular polygon has all its sides equal. D)If a polygon has all its sides equal, then it is regular. 4.Which of the following connectors is the logical conjunction?( ).

A)OR B)AND C)BUT D)Both 5.Which of the following is a counterexample of the conjecture below?

Conjecture: The product of two positive numbers is always greater than either number( ). A)1,2 B)5,2 C)3,10 D)2,-1 46.If∠CFE is an acute angle,what is true.( ).

A)∠CFE is greater than 0 degrees and less than 90 degrees. B)∠CFE is complementary. C)∠CFE is less than 90 degrees. D)∠CFE can not be 110 degrees. 7.What s a conjecture?( ).

A) a guess B) unproven statement based on observations C) switching the hypothesis and conclusion D)a false statement 8.A specific case of when a conjecture is false is called a(n)?( )

A)Counterexample B)Inverse C)Wrong answer D)Negation 9.Write the inverse of the statement in symbolic form.( ) A) ~p → ~q B) t → ~ w C) ~ m → p 10.write the contrapositive of the statement in symbolic form.( ) A) p → q

B) t → ~ w

C) ~ m → p

D) ~ q → ~ p

D) q → p

For the following problems, Find the hypothesis and conclusion in each conditional statement.(8’) 1. If I have finished my homework,then i will go to the movies.

Hypothesis:_________________________; Conclusion:_________________________. 2. If today is Thanksgiving Day, then today is Thursday.

Hypothesis:_________________________; Conclusion:_________________________. 3. All chimpanzees love bananas.

Hypothesis:_________________________; Conclusion:_________________________. 4. Coplaner points lie on the same plane.

Hypothesis:_________________________; Conclusion:_________________________.

Determine if each statement is true or false. If false, provide a counterexample. (4’) 1、If an animal can swim, then it is a fish.

___________________________________________________________________________.

2、If two angles are congruent, then they are right angles.

___________________________________________________________________________.

Write the contrapositive of the statement in words. (6’)

1) If you care enough to send the best, then you send Trademark cards.

___________________________________________________________________________. 2) If you use Trickle deodorant, then you won’t have body odor.

___________________________________________________________________________.

Supply the word,phrase or symbol that can be placed in each blank to make the resulting statement true.(6’) (1)When p is true and q is false ,then p^~q is _____________. (2)When p ?~q is false ，then p is ___________ and q is ______. (3)If the conclusion q is true ,then p→q must be ______.

Use the following to answer questions 1-5:(10’)

p: I love Geometry q:Mrs. Davis is a great teacher r: Mr. Tucker likes Algebra s:Algebra stinks Write the symbolic representation.

1、If I love geometry, then algebra stinks

2、If Mrs. Davis is a great teacher or Mr. Tucker does not like Algebra, then I love Geometry.

3、Algebra stinks if I love Geometry and Mrs. Davis is not a great teacher if Mr. Tucker likes Algebra.

Write the words for each. 4、~p?r

5、(s?r)?q

Write the converse of the statement in words.(6’)

1) If you buy Goal toothpaste, then your children will brush longer.

___________________________________________________________________________ 2) When you serve imported sparkling water, it shows that you have good taste.

___________________________________________________________________________ 3) The man who wears Curtis clothes is well dressed.

___________________________________________________________________________

Inductive or Deductive Reasoning(6’)

1、Sandra learned that if it is cloudy at night it will not be as cold in the morning than if there are no clouds at night. Sandra knows it will be cloudy tonight, so she believes it will not be cold tomorrow morning.

2、In Tom's town, the month of April has had the most rain for the past 5 years. He thinks that April will have the most rain this year.

3、The library charges $0.25 per day for overdue books. Kyle returns a book that is 3 days overdue. Kyle concludes that he will be charged a $0.75 fine.

Extra Questions(15’)

Quadrilateral ABCD satisfies∠ABC=∠ACD=90°，AC=20 and CD=30 Diagonals AC and BD intersect at point E and AE=5 , What is the area of quadrilateral ABCD?

One-inch squares are cut from the corners of this 5 inch square. What is the area in square inches of the largest square that can be fitted into the remaining space?