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QuestionGiven statements pp: Leila practices volleyball and qq: Goran plays piano, express the following: (a) ∼q∨∼p\sim q \vee \sim p (b) ∼p∧∼q\sim p \wedge \sim q (c) p∨∼qp \vee \sim q

Studdy Solution

STEP 1

Assumptions1. The statement pp represents "Leila is practicing volleyball". . The statement qq represents "Goran is playing piano".
3. The symbol ∼\sim represents negation (not).
4. The symbol ∨\vee represents logical OR.
5. The symbol ∧\wedge represents logical AND.

STEP 2

For part (a), the symbolic form is given as ∼q∨∼p\sim q \vee \sim p. This represents the negation of qq OR the negation of pp. In descriptive form, this can be written as "It is not true that Goran is playing piano or Leila is practicing volleyball".∼q∨∼p="It is not true that Goran is playing piano or Leila is practicing volleyball"\sim q \vee \sim p = \text{"It is not true that Goran is playing piano or Leila is practicing volleyball"}

STEP 3

For part (b), the descriptive form is "Goran is not playing piano and Leila is not practicing volleyball". This can be written in symbolic form as the negation of pp AND the negation of qq.
∼p∧∼q="Goran is not playing piano and Leila is not practicing volleyball"\sim p \wedge \sim q = \text{"Goran is not playing piano and Leila is not practicing volleyball"}

STEP 4

For part (c), the descriptive form is "Leila is practicing volleyball or Goran is not playing piano". This can be written in symbolic form as pp OR the negation of qq.
p∨∼q="Leila is practicing volleyball or Goran is not playing piano"p \vee \sim q = \text{"Leila is practicing volleyball or Goran is not playing piano"}

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