Let p and q be the propositions p: It is hot. q: It is raining. Match the English sentences with the compound propositions. It is not hot provided that it is raining. It is hot, unless it is raining. It is either hot or raining (or both). It is hot but not raining. It is raining whenever it is hot. 1. p / q 2. pv q 3. p ^ ¬q 4. p q 5. q→ p 6. qp

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Just started learning proposition and I am struggling a bit with it. Please help identify the correct sign and conditional statement for these two problems.

Let p and q be the propositions
p: It is hot.
q: It is raining.
Match the English sentences with the compound propositions.
It is not hot provided that it
is raining.
It is hot, unless it is raining.
It is either hot or raining (or
both).
It is hot but not raining.
It is raining whenever it is
hot.
1. p Aq
2. pv q
3. p ^ -q
4. p q
5. q-
пр
6. q→ p
Transcribed Image Text:Let p and q be the propositions p: It is hot. q: It is raining. Match the English sentences with the compound propositions. It is not hot provided that it is raining. It is hot, unless it is raining. It is either hot or raining (or both). It is hot but not raining. It is raining whenever it is hot. 1. p Aq 2. pv q 3. p ^ -q 4. p q 5. q- пр 6. q→ p
Let p→→q be the implication
If it is hot then it is raining.
Identify the following English sentences as the conditional statements relative to the
original implication.
<
It is not hot provided that it
is not raining.
It is hot if it is raining.
It is raining if it is hot.
If it is not raining, it is not
hot.
It is not raining whenever it
is not hot.
1. Original implication
2. Converse
3. Contrapositive
4. Inverse
Transcribed Image Text:Let p→→q be the implication If it is hot then it is raining. Identify the following English sentences as the conditional statements relative to the original implication. < It is not hot provided that it is not raining. It is hot if it is raining. It is raining if it is hot. If it is not raining, it is not hot. It is not raining whenever it is not hot. 1. Original implication 2. Converse 3. Contrapositive 4. Inverse
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