Conjunctions and disjunctions

Determine the truth value of the following conjunctions:

1. A square is a 4-sided polygon and a rectangle is a 5-sided polygon
2. $10+7\times 2=72$ and $10\times 7+2=72$
3. March is the third month of the year and December is the last month of the year

$p$: A year has 52 weeks
$q$: December is a summer month
$r$: A kilogram is 1000 grams

1. $p$ ˄ $q$
2. $p$ ˄ $r$
3. $p$ ˄ ~$q$
4. ~$r$ ˄ ~$p$
5. $p$ ˄ ~$q$ ˄ $r$
6. ~$p$ ˄ $q$ ˄ ~$r$

Determine the truth value of the following disjunctions:

1. 1 metre is 100 centimetres or 1 metre is 10 centimetres.
2. A right triangle always has an angle that is 90° degrees or the angles of a square are always 90° degrees.
3. Breakfast is a meal or all meals are breakfasts.

$p$: A week has 5 days
$q$: A day has 24 hours
$r$: An hour has 60 seconds

1. $p$ ˅ $q$
2. $p$ ˅ $r$
3. $p$ ˅ ~$q$
4. ~$r$ ˅ ~$p$
5. ~$p$ ˅ $q$ ˅ ~$r$
6. $p$ ˅ ~$q$ ˅ ~$r$

Let $p$ and $q$ be statement. Fill in the blanks:

1. If $p$ is false, then $p$ ˄ $q$ is _______________.
2. If $p$ is true, then $p$ ˅ $q$ is _______________.
3. If ~$p$ is true, then $p$ ˄ $q$ is _______________.