Compulsory Assignment (Tuesday 22 September 2015)
Exercise 5.1 Prove DeMorgan’s law which states that
You can use the same technique as in the previous example.
Exercise 5.2 Give truth tables for the following:
Exercise 5.3 Consider the following statement:
Alice and Bob are not both ill.
- Define predicate symbols and rewrite the statement in symbolic form.
- Use deMorgan’s law to rephrase the statement.
- Rephrase the statement in English (or Norwegian), using the word ‘well’ rather than ‘ill’ without changing the meaning..
Exercise 5.4 Rewrite the following argument in symbolic form, and decide whether or not it is a valid argument.
- An equilateral triangle (defined as one with three edges of equal length), has three equal angles.
- Triangle has three angles of each.
- Therefore is equilateral.
Exercise 5.5 Rewrite the following argument in symbolic form, and decide whether or not it is a valid argument.
- A triangle is equilateral (defined as above) if and only if it has three equal angles.
- Triangle has three angles of each.
- Therefore is equilateral.
Exercise 5.6 Is the following a valid argument?
- The whale is a fish.
- All fish can swim.
- Therefore the whale can swim.
Exercise 5.7 Is the following a valid argument?
- The whale is not a fish.
- All fish can swim.
- Therefore the whale cannot swim.
Exercise 5.8 Which of the following statements are true and which are false?