Construct a Truth Table for the Statement $\sim(s \vee t) \wedge \sim(t \wedge s)$

question 269

Multiple Choice

Construct a truth table for the statement.
- $\sim(s \vee t) \wedge \sim(t \wedge s)$

• A)
• \(\begin{array}{ccc}
• \mathrm{s} & \mathrm{t} & \sim(\mathrm{s} \vee \mathrm{t}) \wedge \sim(\mathrm{t} \wedge \mathrm{s}) \\
• \hline \mathrm{T} & \mathrm{T} & \mathrm{F} \\
• \mathrm{T} & \mathrm{F} & \mathrm{T} \\
• \mathrm{F} & \mathrm{T} & \mathrm{T} \\
• \mathrm{F} & \mathrm{F} & \mathrm{F}
• \end{array}\)
• B)
• \(\begin{array}{ccc}
• \mathrm{s} & \mathrm{t} & \sim(\mathrm{s} \vee \mathrm{t}) \wedge \sim(\mathrm{t} \wedge \mathrm{s}) \\
• \hline \mathrm{T} & \mathrm{T} & \mathrm{F} \\
• \mathrm{T} & \mathrm{F} & \mathrm{F} \\
• \mathrm{F} & \mathrm{T} & \mathrm{F} \\
• \mathrm{F} & \mathrm{F} & \mathrm{F}
• \end{array}\)
• C)
• \(\begin{array}{ccc}
• \mathrm{s} & \mathrm{t} & \sim(\mathrm{s} \vee \mathrm{t}) \wedge \sim(\mathrm{t} \wedge \mathrm{s}) \\
• \hline \mathrm{T} & \mathrm{T} & \mathrm{F} \\
• \mathrm{T} & \mathrm{F} & \mathrm{F} \\
• \mathrm{F} & \mathrm{T} & \mathrm{T} \\
• \mathrm{F} & \mathrm{F} & \mathrm{F}
• \end{array}\)
• D)
• \(\begin{array}{ccc}
• \mathrm{s} & \mathrm{t} & \sim(\mathrm{s} \vee \mathrm{t}) \wedge \sim(\mathrm{t} \wedge \mathrm{s}) \\
• \hline \mathrm{T} & \mathrm{T} & \mathrm{F} \\
• \mathrm{T} & \mathrm{F} & \mathrm{F} \\
• \mathrm{F} & \mathrm{T} & \mathrm{F} \\
• \mathrm{F} & \mathrm{F} & \mathrm{T}
• \end{array}\)

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Definitions:

Divide-And-Conquer

An algorithm design paradigm based on recursively breaking down a problem into two or more sub-problems of the same or related type until these become simple enough to be solved directly.

Design Approach

A design approach refers to the strategy or methodology applied during the problem-solving and planning phase of developing software, systems, or products, focusing on meeting specific goals and requirements.

Smaller Problems

A concept in programming and algorithm design that involves breaking a problem down into more manageable sub-problems.

Local Variables

Variables that are declared inside a function or block and are accessible only within that function or block.