Underline the hypothesis (p) once and the conclusion (q) twice.  Be able to write each in ìif-thenî form.
Tell whether each is true or false.

1.  If a man lives in London, then he lives in England.

2.  It is sufficient for a triangle to be equilateral for it to be isosceles.

3.  It is necessary for an animal to have four legs for it to be a normal cat.

4.  Two triangles are congruent only if their corresponding angles have equal measures.

5.  2 is a factor of the square of an integer, if 2 is a factor of the integer.

6.  That 6 is a factor of the square of an integer follows from 6 being a factor of the integer.
 

State the converse of each statement above. Tell whether each is true or false.

7.
 
8.

9.

10.

11.

12.
 

State the contrapositive of each statement above. Tell whether each is true or false.

13.

14.

15.

16.

17.

18.
 

State the negation of each statement below.  Tell whether the negation is true or false.

19.  Algebra is a branch of mathematics.

20.  Scientists are not uneducated.

21.  1 belongs to the set of integers and to the set of positive numbers.

22.  1 belongs to the set of integers or to the set of negative numbers.

23.  Some equations have real roots.

24.  All equations have at least one real root.

25.  If a number is an integer, then it is greater than 0.
 

Translation:  Use A for Argentina mobilizes and E for Ecuador mobilizes, etc.

26.  Argentina mobilizes and Ecuador mobilizes.

27.  Both Argentina and Ecuador mobilize.

28.  Either Argentina or Ecuador mobilizes.

29.  Neither Argentina nor Ecuador mobilizes.

30.  Argentina and Ecuador do not both mobilize.

31.  Argentina and Ecuador both do not mobilize.

32.  Argentina or Ecuador mobilizes, but they donít both mobilize.

33.  Argentina mobilizes and either Brazil declares an embargo, or Cuba continues to send arms to South America.

34.  Either Argentina mobilizes and Brazil declares an embargo or Cuba continues to send arms to South America.

35.  Argentina does not mobilize, but Brazil declares an embargo.

36.  It is not the case that both Argentina mobilizes and Brazil declares an embargo.

37.  Either Argentina mobilizes and Brazil declares an embargo or it is not the case both that Cuba continues to send arms into South America and that the Dominican Republic appeals to the UN.
 

38.  Either Brazil declares an embargo and the Dominican Republic appeals to the UN or either Cuba continues to send arms to South America or Argentina mobilizes.
 

39.  If Cuba continues to send arms to South America, then either Argentina will mobilize or the Dominican Republic will appeal to the UN.
 

40.  If the Dominican Republic appeals to the UN, then if Ecuador mobilizes, Argentina does.

41.  If Brazil declares an embargo, then Ecuador mobilizes only if Argentina does.

42.  If Cuba stops sending arms to South America, then neither Argentina nor Ecuador mobilizes.