Question

If \[p:\] “roses are red” and \[q:\] “the sun is a star”. Then what is the verbal translation of \[\left( {\sim p} \right) \vee q\]?
A. roses are not red and the sun is not a star
B. it is not true that roses are red or the sun is not a star
C. it is not true that roses are red and the sun is a star
D. roses are not red or the sun is a star
E. it is not true that roses are red and the sun is a star

Answer 1

Hint: In the given question, two statements are given. First, find the meaning of given mathematical logical symbols. Then convert the symbols into verbal translation.

Formula used:
Meaning of logical symbols are:
\[\sim \]: Negation
\[ \vee :\] or

Complete step by step solution:
The given statements are:
   \[p:\] “roses are red”
   \[q:\] “the sun is a star”
Let’s find the verbal translation of \[\left( {\sim p} \right) \vee q\].
There is a negation sign present in front of \[p\].
So, \[\left( {\sim p} \right):\] “roses are not red”
The meaning of \[ \vee \] in mathematical logic is or.
Therefore, the verbal translation of \[\left( {\sim p} \right) \vee q\] is,
“roses are not red or the sun is a star”
Hence the correct option is option D.

Note: Students often confused with the sign \[ \wedge \] and \[ \vee \].
Meaning of \[p \wedge q\] is \[p\] and \[q\].
Meaning of \[p \vee q\] is \[p\] or \[q\].