Using the letters indicated for the component statements, translate the following compound statements into symbolic notation. a. A: the tractor wins; B: the truck wins; C: the race will be exciting. Whether the tractor wins or the truck wins, the race will be exciting b. A: snow; B: rain; C: yesterday was cloudy Yesterday was cloudy but there was neither snow nor rain. c. A: Koalas will be saved; B: climate change is addressed; C: rising water levels Koalas will be saved only if climate change is addressed; furthermore, failure to address climate change will cause rising water levels. d. A: the city’s economy will improve; B: a strong school system The city’s economy will improve conditional upon a strong school system. e. A: the city’s economy will improve; B: a strong school system A strong school system is a necessary condition for the city’s economy to improve.

Construct truth tables for the following wffs. Note any tautologies or contradictions. a. $(A \rightarrow B) \leftrightarrow A^{\prime} \vee B$ b. $(A \wedge B) \vee C \rightarrow A \wedge(B \vee C)$ c. $A \wedge\left(A^{\prime} \vee B^{\prime}\right)^{\prime}$ d. $A \wedge B \rightarrow A^{\prime}$ e. $(A \rightarrow B) \rightarrow[(A \vee C) \rightarrow(B \vee C)]$

The vertices of a sandbox are P(12,14), Q(12,17), R(16,17), and S(16,14). The coordinates are measured in feet. What is the perimeter of the sandbox?