Answer :
Answer:
a) [tex]p\rightarrow \neg q \wedge \neg r[/tex]
b) [tex]r\vee q \iff \neg p[/tex]
Step-by-step explanation:
Given statements:
[tex]p:[/tex] It is raining
[tex]q:[/tex] Sam is wearing a hat
[tex]r:[/tex] It is winter
To find:
The symbolic forms for the following:
a) If it is raining then Sam is not wearing a hat, and it is not winter.
b) It is winter or Sam is wearing a hat, if and only if it is not raining.
Solution:
a) The statement followed by 'if ' is written on the left hand side and the statement followed by 'then' is written after the symbol [tex]\rightarrow .[/tex]
Not of a statement [tex]s[/tex] is represented as [tex]\neg s[/tex].
And is represented by [tex]\wedge[/tex] symbol.
Therefore, the statement in symbolic form becomes:
[tex]p\rightarrow \neg q \wedge \neg r[/tex]
b) Not of a statement [tex]s[/tex] is represented as [tex]\neg s[/tex].
Or is represented by [tex]\vee[/tex] symbol.
If and only if is represented by the symbol [tex]\iff.[/tex]
Therefore, the statement in the symbolic form becomes:
[tex]r\vee q \iff \neg p[/tex]