Questions: The company budgets more money for support than engineering. The company budgets the least amount of money for research. (a) Write the following statement in symbolic form using p and q. The company budgets more money for support than engineering, or the company budgets the least amount of money for research. Symbolic form: [] (b) Based on the information in the circle graph, complete the table to determine the truth of the statement from part (a). Use T for true and F for false. p q [] Research 40,000 Support 145,000 Sales 15,000 Engineering 100,000

The company budgets more money for support than engineering. The company budgets the least amount of money for research. (a) Write the following statement in symbolic form using p and q. The company budgets more money for support than engineering, or the company budgets the least amount of money for research. Symbolic form: [] (b) Based on the information in the circle graph, complete the table to determine the truth of the statement from part (a). Use T for true and F for false. p q [] Research 40,000 Support 145,000 Sales 15,000 Engineering 100,000
Transcript text: The company budgets more money for support than engineering. The company budgets the least amount of money for research. (a) Write the following statement in symbolic form using p and q. The company budgets more money for support than engineering, or the company budgets the least amount of money for research. Symbolic form: [] (b) Based on the information in the circle graph, complete the table to determine the truth of the statement from part (a). Use T for true and F for false. p q [] Research $40,000 Support $145,000 Sales $15,000 Engineering $100,000
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Solution

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Solution Steps

Step 1: Find the symbolic form

The given statement is "The company budgets more money for support than engineering, or the company budgets the least amount of money for research." This statement uses the conjunction "or" to connect two propositions, _p_ and _q_. Therefore, its symbolic form is $p \lor q$.

Step 2: Determine the truth value of _p_

_p_ is defined as "The company budgets more money for support than engineering." The support budget is $145,000, and the engineering budget is $100,000. Since $145,000 > $100,000, proposition _p_ is true.

Step 3: Determine the truth value of _q_

_q_ is defined as "The company budgets the least amount of money for research." The research budget is $40,000, the sales budget is $115,000, the support budget is $145,000, and the engineering budget is $100,000. Since $40,000 is the smallest budget, the proposition _q_ is true.

Final Answer

(a) $p \lor q$ (b) | _p_ | _q_ | $p \lor q$ | |---|---|---| | T | T | T |

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