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Ms. D’Amato & Ms. Reeves                                                   Block:

                                    Deductive Reasoning

Review of Conditional Statements:


                     Conditional:

                     Converse:

                     Inverse:

                     Contrapositive:


Given the symbolic notation, ~c → ~d, complete the following:

                             Converse
                              Inverse
                           Contrapositive


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Law of Detachment. If p  q is true and
                          p is true, then q
                          must be true.




Example 1: Assume that “If Tim studies, then he passes” is a true statement. Also, assume
            true that “Tim studies.” What conclusion can you make?




Example 2: Assume that “If two lines are parallel then they never meet.” Also, assume that “AB
            and CD are parallel. What conclusion can you make?
Directions: If possible, write a conclusion for the argument. If a conclusion is not
possible, write INVALID.

1. If mA = 45, then A is acute. The measure of A = 45,




2. If it is raining, then the sidewalk is wet. The sidewalk is wet.




Law of Syllogism:    If p  q is true and
                           q  r is true,
                           then p  r is true.




Example 3: If Jack goes to the mall, then Jill will go to the mall.
           If Jill goes to the mall, then Pam will go to the mall.

     Assume the two statements are true. What conclusion can you make?




Example 4: If a number is a multiple of 54, then it is a multiple of 18.
           If a number is a multiple of 18, then it is a multiple of 6.

     Assume the two statements are true. What conclusion can you make?




Directions: Write a conclusion using the Law of Syllogism.

           If two angles are vertical, then the angles are congruent.
           If the angles are congruent, then their measures are equal.
Examples: Determine if a conclusion can be made from the given statements. If a
conclusion can be made, state the conclusion then state which law was used, the Law of
Detachment, Law of Syllogism, or with a combination of contrapositive. If a conclusion
cannot be made, state INVALID.

1.   rt                              2. b  q                  3. t  k
     r                                   q  r                     k




4. s  p                            5. b  t                  6. p  q
   p  r                                t                          p  r




7. s  p                            8. bt
   p  r                                b r
   rt                                   sr




Factor the following using the GCF:

1.) 4xy3 + 16x2y2                     2.) 55x2 – 11x7 + 44x5     3.) 30x – 6x2

				
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