Let p, q, and r represent the following simple statements. p: It is snowing outside. q: It is cold. r: It is cloudy. Write the following compound statement in its symbolic form. If it is snowing outside, then it is cold or it is not cloudy.
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p:
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It is snowing outside.
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q:
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It is cold.
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r:
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It is cloudy.
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Sol:-
The given compound statement is:
"If it is snowing outside, then it is cold or it is not cloudy."
To represent this statement in symbolic form, we need to break it down into simple statements and logical operators. Let's define the following simple statements:
p: It is snowing outside. q: It is cold. r: It is cloudy.
The first part of the statement is "If it is snowing outside." This can be represented using the conditional operator "→" as:
p → (q ∨ ¬r)
The arrow "→" is read as "if...then". It means that if the statement p is true (i.e., it is snowing outside), then the statement q ∨ ¬r must also be true. The symbol "∨" represents "or", and the symbol "¬" represents "not". So, q ∨ ¬r means "It is cold or it is not cloudy."
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