Question

Consider a propositional language where:

A =“Simi comes to the party”
B =“Marike comes to the party”
C =“Elton comes to the party”
D =“Vuyo comes to the party”
Which of the below mathematical statements/propositions is the correct equivalent of the English sentence “If Vuyo comes to the party, then Marike and Elton come too” ?
Question 4 options:

D ↔ (C ∧ ¬A)



D → (¬C → A)



D → B ∧ C



C → ¬A ∧ ¬B

Answer 1

The English sentence “If Vuyo comes to the party, then Marike and Elton come too” can be translated into propositional logic as follows:

- Let D represent "Vuyo comes to the party"
- Let B represent "Marike comes to the party"
- Let C represent "Elton comes to the party"

The sentence can be interpreted as:

- If D (Vuyo comes), then both B (Marike comes) and C (Elton comes).

In logical notation, this can be expressed as:

**D → (B ∧ C)**

Now let's look at the provided options to find the correct equivalent:

1. D ↔ (C ∧ ¬A)
2. D → (¬C → A)
3. D → (B ∧ C)
4. C → (¬A ∧ ¬B)

Among these options, option 3:

**D → (B ∧ C)**

is the correct equivalent of the English sentence.