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The propositional variables f, h, and p represent the propositions:___________f: The student got an A on the final.h: The student turned in all the homework.p: The student is on academic probationSelect the logical expression that represents the statement: "The student is not on academic probation and the student got an A on the final or turned in all the homework."

Respuesta :

The options are:

[tex](A)\neg p \land (f \lor h)\\(B)(\neg p \land f) \lor h\\(C)\neg p \land f \land h\\(D)\neg( p \land f) \lor h[/tex]

Answer:

[tex](B)(\neg p \land f) \lor h[/tex]

Explanation:

Given the propositional variables:

  • f: The student got an A on the final.
  • h: The student turned in all the homework.
  • p: The student is on academic probation

The negation of p, [tex]\neg p=$The student is not on academic probation[/tex]

  • A AND B (Logical conjunction) is written as: [tex]A \land B[/tex]
  • A OR B (Logical disjunction) is written as: [tex]A \lor B[/tex]

Therefore, the logical expression for the statement:

"The student is not on academic probation and the student got an A on the final " is: [tex]\neg p \land f[/tex]

Therefore, the logical expression for the given statement

"The student is not on academic probation and the student got an A on the final or turned in all the homework."

is: [tex](\neg p \land f) \lor h[/tex]

The correct option is B.

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