4.1.4.4. Disjunctive Syllogism

Try these first

1. 1.

   If I say 'It is either snowing or sunny' and it is not snowing, what can we conclude?

   Hint

   Use the structure of disjunctive syllogism.

2. 2.

   If the statement is 'A dog or a cat is outside' and I know the dog is not outside, what can I conclude?

   Hint

   Look at the disjunction.

3. 3.

   If 'p or q' is true and '¬p' is true, what can we conclude?

   • p is true
   • q is true
   • Both p and q are false

   Hint

   Think about the nature of the disjunction.

4. 4.

   The statement 'If p, then q' represents what type of argument?

   • True
   • False

   Hint

   Recall your definitions.

5. 5.

   Create a complex logical statement using disjunctions and demonstrate its validity using Disjunctive Syllogism.

   Hint

   Incorporate multiple premises and show negation.

6. 6.

   Analyze this argument: If either x is true or y is true, but x is false, then what can we conclude about y?

   Hint

   Apply Disjunctive Syllogism directly.