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
Express the following switching circuit in symbolic form of logic. Construct the switching table.
The dual of statement \( t \lor (p \lor q) \) is _________.
The slope of the tangent to the curve \( x = \sin\theta \) and \( y = \cos 2\theta \) at \( \theta = \frac{\pi}{6} \) is ___________.
Solve the following L.P.P. by graphical method:
Maximize:
\[ z = 10x + 25y. \] Subject to: \[ 0 \leq x \leq 3, \quad 0 \leq y \leq 3, \quad x + y \leq 5. \]