LOGIC AND REASONING PRACTICE PAPER

LOGIC AND REASONING PRACTICE PAPER2015

1. Let , , . Translate each of the following English statements into formal logical statements using symbols.

a) It is raining whenever the ground is wet.b) It is not true that it is raining or the ground is wet.c) The ground is wet if it is raining and it is cloudy.d) It only rains at night.e) If its not the case that the ground is wet and it is raining, then it is not cloudy.

2. are the propositions: you get a Grade in Mathematics: you do all logic questions: you revise your work regularly

i) Using and and logical connectives, state the converse, contrapositive and the inverse of the proposition ii) Express as an English sentence.

3. Four propositions and which relate to entries in a contest, are defined below.

w: entry includes the contestants work telephone numberx: entry includes the contestants addressy:entry includes the contestants home telephone numberz:entry includes the contestants name

Express the following statements in terms w, x, y and z and the logical connectives and .

a) Entry includes the contestants name and addressb) Entry does not include the contestants home and work telephone numbersc) Entry includes at least one of the contestants address and home telephone number.

4. Let represent the proposition You have your cake, which may be considered equivalent to You do not eat your cake in this question.

i) Express the proposition You have your cake and eat it in symbolic form.ii) Hence, with the aid of a truth table explain why the proposition You have your cake and eat it is a contradiction.

5. State whether each of the following is the converse, inverse or contrapositive of the proposition .a. b. c.

6. Write the converse, inverse and contrapositive of the following sentences.a. If you pay a subscription fee, then you can access the website.b. I go to beach whenever it is a sunny summer day.c. It rains if it is a weekend day

7. By using the laws of algebra of propositions, show that each of the following are logically equivalent.

a) and b) and c) and d) and

8. Decide whether each of the following is a tautology, contradiction or a contingency, using truth tables. [Include a statement at the end of each, explaining your answer.]

a) b) c)

9. Use a truth table to show that .