Step 1: Understanding Logical Operators
- \( p \rightarrow q \) means "If \( p \), then \( q \)".
- \( \land \) represents logical AND.
- \( \rightarrow \) represents logical implication.
Step 2: Constructing the Truth Table

The dual of statement \( t \lor (p \lor q) \) is _________.
The principal solutions of the equation \( \cos\theta = \frac{1}{2} \) are _________.
If \( \alpha, \beta, \gamma \) are direction angles of a line and \( \alpha = 60^\circ, \beta = 45^\circ \), then \( \gamma \) is _________.
The perpendicular distance of the plane \( r \cdot (3\hat{i} + 4\hat{j} + 12\hat{k}) = 78 \) from the origin is __________.
The slope of the tangent to the curve \( x = \sin\theta \) and \( y = \cos 2\theta \) at \( \theta = \frac{\pi}{6} \) is ___________.