Disjunction

Disjunction

How to solve the disjunction of two statements problems: its truth values, examples, and their solutions.

Truth Value

p disjunction q is true if either p or q is true.

pq is the disjunction of p and q.

It means 'p or q'.

So pq is true
if either p or q is true.

This is the difference between
the truth value of a conjunction: pq.

Example 1

The symbols represent statements: p: 5 is a positive number. q: 1 + 1 = 3. Find the truth value for 'p disjunction q'.

'p: 5 is a positive number' is true.

So 'pq' is true.

You don't need to find the truth value of q,
because 'p is true' is enough to make pq true.

Example 2

The symbols represent statements: q: 1 + 1 = 3. r: 2 > 9. Find the truth value for 'q disjunction r'.

'q: 1 + 1 = 3' is false.

'r: 2 > 9' is false.

So 'qr' is false.