Questions: A university released figures on the majors chosen by its incoming freshmen. The circle graph shows this year's numbers for five majors. Nursing 480 Math 120 History 340 Business 220 Biology 1290 Consider statements p and q. p: History was chosen by the fewest number of freshmen. q: Fewer freshmen chose to major in business than in nursing. (a) Write the following statement in symbolic form using p and q: History was chosen by the fewest number of freshmen, and fewer freshmen chose to major in business than in nursing. 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 []

A university released figures on the majors chosen by its incoming freshmen. The circle graph shows this year's numbers for five majors. Nursing 480 Math 120 History 340 Business 220 Biology 1290 Consider statements p and q. p: History was chosen by the fewest number of freshmen. q: Fewer freshmen chose to major in business than in nursing. (a) Write the following statement in symbolic form using p and q: History was chosen by the fewest number of freshmen, and fewer freshmen chose to major in business than in nursing. 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 []
Transcript text: A university released figures on the majors chosen by its incoming freshmen. The circle graph shows this year's numbers for five majors. Nursing 480 Math 120 History 340 Business 220 Biology 1290 Consider statements p and q. p: History was chosen by the fewest number of freshmen. q: Fewer freshmen chose to major in business than in nursing. (a) Write the following statement in symbolic form using p and q: History was chosen by the fewest number of freshmen, and fewer freshmen chose to major in business than in nursing. 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 []
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Solution

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Solution Steps

Step 1: Analyze the provided statements

Given statements _p_ and _q_:

  • _p_: History was chosen by the fewest number of freshmen.
  • _q_: Fewer freshmen chose to major in business than in nursing.

We are asked to symbolize the statement: "History was chosen by the fewest number of freshmen, and fewer freshmen chose to major in business than in nursing."

Step 2: Symbolize the statement

The given statement is a conjunction of _p_ and _q_. The word "and" indicates a conjunction, which is represented by the symbol $\wedge$.

Step 3: Construct the symbolic form

Therefore, the symbolic form of the statement is $p \wedge q$.

Final Answer: $p \wedge q$

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