Express the following propositions in symbolic form, and identify the principal connective: i.Either Karen is studying computing and Ketsi is not studying mathematics, or Ketsi is studying mathematics. ii.It is not the case case that if it is sunny then i will carry an umbrella.

Express the following propositions in symbolic form, and identify the principal connective: i.Either Karen is studying computing and Ketsi is not studying mathematics, or Ketsi is studying mathematics. ii.It is not the case case that if it is sunny then i will carry an umbrella.

Question
Upper Level Math
asked 2021-02-03
Express the following propositions in symbolic form, and identify the principal connective:
i.Either Karen is studying computing and Ketsi is not studying mathematics, or Ketsi is studying mathematics.
ii.It is not the case case that if it is sunny then i will carry an umbrella.

Answers (1)

2021-02-04
Step 1
(i)
Let,
p:Karen is studying computing.
q:Ketsi is studying mathematics.
\(\displaystyle\sim{q}\):Ketsi is now studying mathematics.
Then,\(\displaystyle{\left({p}\wedge!{q}\right)}\vee{q}\):Either Karen is studying computing and Ketsi is not mathematics, or Ketsi is studying mathematics.
Here, principal connective is "vv"(i.e."or").
Step 2
(ii)
Let,
p: It is sunny.
q: I will carry an umberella.
Then, \(\displaystyle!{\left({p}\rightarrow{q}\right)}\): It is not the case that if it is sunny then i will carry an umbrella.
Here, principal connective is "\(\displaystyle\sim\)"(i.e."not").
0

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