# 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.
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Corben Pittman
Step 1
(i)
Let,
p:Karen is studying computing.
q:Ketsi is studying mathematics.
$\sim q$:Ketsi is now studying mathematics.
Then,$\left(p\wedge !q\right)\vee q$: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, $!\left(p\to q\right)$: It is not the case that if it is sunny then i will carry an umbrella.
Here, principal connective is "$\sim$"(i.e."not").