Let's go through each part step-by-step to express the given statements in words.
Given:
- [tex]\( p \)[/tex]: demand is increasing
- [tex]\( q \)[/tex]: supply is decreasing
Now, we need to convert the logical statements into words:
### a) [tex]\(\sim p\)[/tex]
The symbol [tex]\(\sim\)[/tex] represents logical negation (i.e., "not").
- [tex]\(\sim p\)[/tex]: "not demand is increasing"
- In simple words, this means that demand is not increasing.
### b) [tex]\(\sim q\)[/tex]
Again, the symbol [tex]\(\sim\)[/tex] represents logical negation.
- [tex]\(\sim q\)[/tex]: "not supply is decreasing"
- In simple words, this means that supply is not decreasing.
### e) [tex]\(\sim p \wedge q\)[/tex]
The symbol [tex]\(\wedge\)[/tex] represents logical conjunction (i.e., "and").
- [tex]\(\sim p \wedge q\)[/tex]: "not demand is increasing and supply is decreasing"
- In simple words, this means that demand is not increasing, and supply is decreasing at the same time.
### f) [tex]\(p \vee \sim q\)[/tex]
The symbol [tex]\(\vee\)[/tex] represents logical disjunction (i.e., "or").
- [tex]\(p \vee \sim q\)[/tex]: "demand is increasing or not supply is decreasing"
- In simple words, this means that either demand is increasing, or supply is not decreasing.
### c) [tex]\(p \wedge q\)[/tex]
Again, the symbol [tex]\(\wedge\)[/tex] represents logical conjunction.
- [tex]\(p \wedge q\)[/tex]: "demand is increasing and supply is decreasing"
- In simple words, this means that demand is increasing and supply is decreasing at the same time.
### g) [tex]\(\sim p \wedge \sim q\)[/tex]
- [tex]\(\sim p \wedge \sim q\)[/tex]: "not demand is increasing and not supply is decreasing"
- In simple words, this means that demand is not increasing, and supply is also not decreasing.
These are the steps to express each of the given logical statements into words:
#### Final Answers:
a) [tex]\(\sim p\)[/tex]: "demand is not increasing"
b) [tex]\(\sim q\)[/tex]: "supply is not decreasing"
e) [tex]\(\sim p \wedge q\)[/tex]: "demand is not increasing and supply is decreasing"
f) [tex]\(p \vee \sim q\)[/tex]: "demand is increasing or supply is not decreasing"
c) [tex]\(p \wedge q\)[/tex]: "demand is increasing and supply is decreasing"
g) [tex]\(\sim p \wedge \sim q\)[/tex]: "demand is not increasing and supply is not decreasing"
