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Write the negation of the statement

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1. Write the negation of the statement. Start the negation with the word "Some," "No," or "All."

   All classic movies were first produced in black and white.

2. Use an Euler diagram to determine whether the argument is valid or invalid.

   	All frogs are poetical.
   	Kermit is a frog.
   ∴	Kermit is poetical.

   Choose the Euler diagram that shows whether the argument is valid or invalid.

   

   There are two labeled circles and a single labeled point inside a rectangle. The two circles are labeled Frogs and Poetical. The point is labeled K.
   • The Frogs circle is completely inside the Poetical circle.
   • Point K is located inside the Poetical circle, but not inside the Frogs circle.

    

   

   There are two labeled circles and a single labeled point inside a rectangle. The two circles are labeled Frogs and Poetical. The point is labeled K.
   • The Poetical circle is completely inside the Frogs circle.
   • Point K is located inside the Poetical circle.

    

   

   There are two labeled circles and a single labeled point inside a rectangle. The two circles are labeled Frogs and Poetical. The point is labeled K.
   • The Frogs circle partially overlaps the Poetical circle.
   • Point K is located inside the intersection of the two circles.

    

   

   There are two labeled circles and a single labeled point inside a rectangle. The two circles are labeled Frogs and Poetical. The point is labeled K.
   • The Frogs circle is completely inside the Poetical circle.
   • Point K is located inside the Frogs circle.

   
   

   Is the argument valid or invalid?

3. Use an Euler diagram to determine whether the argument is valid or invalid.

   	No rocker would do the Mariachi.
   	All baseball fans do the Mariachi.
   ∴	No rocker is a baseball fan.

   Choose the Euler diagram that shows whether the argument is valid or invalid.

   

   There are three labeled circles and a single labeled point inside a rectangle. The circles are labeled Rockers, Mariachi, and Baseball. The point is labeled R.
   • The Baseball circle is completely inside the Mariachi circle.
   • The Rockers circle doesn't overlap either of the other two circles.
   • The point R is located inside the Rockers circle.

    

   

   There are three labeled circles and a single labeled point inside a rectangle. The circles are labeled Rockers, Mariachi, and Baseball. The point is labeled R.
   • The Baseball circle is completely inside the Mariachi circle.
   • The Rockers circle doesn't overlap either of the other two circles.
   • The point R is located inside the Baseball circle.

    

   

   There are three labeled circles and a single labeled point inside a rectangle. The circles are labeled Rockers, Mariachi, and Baseball. The point is labeled R.
   • The Baseball circle is completely inside the Mariachi circle.
   • The Rockers circle partially overlaps the other two circles.
   • The point R is located inside the Rockers circle, but not inside the Baseball nor the Mariachi circles.

    

   

   There are three labeled circles and a single labeled point inside a rectangle. The circles are labeled Rockers, Mariachi, and Baseball. The point is labeled R.
   • The Mariachi circle is completely inside the Baseball circle.
   • The Rockers circle doesn't overlap either of the other two circles.
   • The point R is located inside the Rockers circle.

   
   

   Is the argument valid or invalid?

4. Use an Euler diagram to determine whether the argument is valid or invalid.

   	All men behave badly.
   	Some hockey players behave badly.
   ∴	Some hockey players are men.

   Choose the Euler diagram that shows whether the argument is valid or invalid.

   

   There are three labeled circles and a single labeled point inside a rectangle. The three circles are labeled Behave badly, Men, and Hockey. The point is labeled H.
   • The Men circle is completely inside the Behave badly circle.
   • The Hockey circle partially overlaps the Behave badly circle, but does not overlap the Men circle.
   • Point H is located inside the intersection of the Hockey and Behave badly circles.

    

   

   There are three labeled circles and a single labeled point inside a rectangle. The three circles are labeled Behave badly, Men, and Hockey. The point is labeled H.
   • The Hockey circle is completely inside the Men circle.
   • The Behave badly circle partially overlaps the Men circle, but does not overlap the Hockey circle.
   • Point H is located inside the intersection of the Behave badly and Men circles.

5. Use an Euler diagram to determine whether the argument is valid or invalid.

   	All prime numbers are odd.
   	2 is a prime number.
   ∴	2 is an odd number.

   Choose the Euler diagram that shows whether the argument is valid or invalid.

6. Use all of the premises in the argument to determine a valid conclusion for the argument.

   	All cats are strange.
   	Boomer is not strange.

7. Examine the following three premises.

8. All people who have an Xbox play video games.
9. All people who play video games enjoy life.
10. Some mathematics professors enjoy life.

11. Now consider each of the following six conclusions. For each conclusion, determine whether the argument formed by the three premises and the conclusion is valid or invalid.

    (a)

    ∴ Some mathematics professors have an Xbox.

    validinvalid    

    (b)

    ∴ Some mathematics professors play video games.

    validinvalid    

    (c)

    ∴ Some people who play video games are mathematics professors.

    validinvalid    

    (d)

    ∴ Mathematics professors never play video games.

    validinvalid    

    (e)

    ∴ All people who have an Xbox enjoy life.

    validinvalid    

    (f)

    ∴ Some people who enjoy life are mathematics professors.

    validinvalid    

12. Use an Euler diagram and all of the premises in the following argument to determine a valid conclusion for the argument. (See Example 7 in this section.)

    	All journalists are writers.
    	No writers are scientists.

13. A survey asked students which team sport they preferred to watch. The results are in the following Venn diagram with H representing hockey, S representing soccer, and F representing football. (See Example 9 in this section.)

    

    76
    142
    83
    55
    126
    148
    56
    A diagram is composed of three overlapping circles contained in the interior of a rectangle. The top circle is labeled H, the left circle is labeled F and the right circle is labeled S. Numbers are given in different regions. They are listed as follows:

    • H region not including F and S: 76
    • H region overlapping with F but not S: 142
    • H region overlapping with S but not F: 83
    • All 3 regions overlapping: 55
    • F region not including H and S: 126
    • S region not including H and F: 56
    • F region overlapping with S but not H: 148
    (a)

    How many people preferred exactly one sport?

    258  people
    (b)

    How many people liked all three sports?

    55  people
    (c)

    How many people preferred hockey and football but not soccer?

    142  people
    (d)

    How many people liked exactly two of the sports?

    373  people
    (e)

    If 800 people were surveyed, how many people did not like any of the sports?

    A test for a performance-enhancing drug is given to 200 athletes. The results are shown in the following Venn diagram. (See Example 11 in this section.)

    

    15

    30

    11

    144

    A diagram is composed of two overlapping circles contained in the interior of a rectangle. The leftmost circle is labeled "Has banned drug" and the rightmost circle is labeled "Athlete tests positive (P)". Numbers are given in different regions. They are listed as follows:

    • "Has banned drug" not overlapping with "Athlete tests positive (P)": 15
    • "Athlete tests positive (P)" not overlapping with "Has banned drug": 11
    • "Has banned drug" overlapping with "Athlete tests positive (P)": 30
    • Region in the rectangle outside both circles: 144

    Using the Venn diagram, complete the following table.

     

    	Positive Test	Negative Test
    Athlete Has Banned Drug