Construct a Truth Table for the Statement $(\sim p \rightarrow q) \rightarrow(q \rightarrow \sim r)$

question 240

Multiple Choice

Construct a truth table for the statement.
- $(\sim p \rightarrow q) \rightarrow(q \rightarrow \sim r)$

• A) \(\begin{array}{cccc} \mathrm{p} & \mathrm{q} & \mathrm{r} & (\sim \mathrm{p} \rightarrow \mathrm{q}) \leftrightarrow(\mathrm{q} \rightarrow \sim \mathrm{r}) \\ \hline \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{F} \\ \mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{F} \\ \mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} \\ \mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{T} \\ \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{F} \\ \mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{F} \\ \mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{F} \\ \mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{F} \end{array}\)
• B) \(\begin{array}{cccc} \mathrm{p} & \mathrm{q} & \mathrm{r} & (\sim \mathrm{p} \rightarrow \mathrm{q}) \leftrightarrow(\mathrm{q} \rightarrow \sim \mathrm{r}) \\ \hline \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{F} \\ \mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{T} \\ \mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} \\ \mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{T} \\ \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{F} \\ \mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{T} \\ \mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T} \\ \mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{T} \end{array}\)

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Definitions:

Heritability

A measure of how much of the variation in a trait among individuals within a population can be attributed to genetic differences.

Twins

Two individuals born from the same pregnancy, who can be either identical (from one egg) or fraternal (from two different eggs).

Adopted Children

Children who have been legally taken and raised by parents who are not their biological parents.

Heritability

The proportion of variation in traits among individuals that can be attributed to genetic factors.