4.1.4.3. Transitive Law (Hypothetical Syllogism)

Try these first

1. 1.

   What is the transitive law?

   Hint

   Think about how one condition leads to another.

2. 2.

   State the meaning of Modus Ponens.

   Hint

   Recall the structure of this rule.

3. 3.

   What does the transitive law state?

   • If p equals q
   • If p implies q and q implies r
   • then p implies r
   • None of the above

   Hint

   Consider the structure of conditional statements.

4. 4.

   Is the following statement a tautology: 'If p and q are both true then p must be true'?

   • True
   • False

   Hint

   Think about the implications of 'p and q'.

5. 5.

   Given the statements: 'If a book is read, knowledge is gained; If knowledge is gained, confidence increases.' Prove the transitive law in this context.

   Hint

   Identify p, q, and r in your reasoning.

6. 6.

   Construct a truth table for the transitive law that includes all variable combinations for p, q, and r.

   Hint

   Show how the implications relate truthfully.