Question

The statement pattern \([(p∧q)\rightarrow (\sim p∨r)]∨[(\sim p∨r)\rightarrow (p∧q)]\) is

• A. a contradiction
• B. a tautology
• C. equivalent to \((p∧q)∨r\).
• D. equivalent to \((p∨q)\) .

Hint:

Find the length of tangent and radius, then use the half angle sine.

Answer 1

The Correct Option is B

Step 1: Length of tangent:
Length of tangent from the origin = $\sqrt{49 + 1 - 25} = 5$.

Step 2: Triangle:
The tangent length equals the radius (both 5), so the two tangent points and the centre and origin form a square. So the tangents are perpendicular, $90^\circ$ (B).

Final Answer:
$90^\circ$. \[ \boxed{90^{\circ}} \]