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Consider the following statements : p:...

Consider the following statements :
p: He is intelligent
q: He is strong
Then symbolic form of statements 'it is wrong that he is intelligent or strong's

A

`~p vv~q`

B

`~pvvq`

C

`~p^^~q`

D

`p^^~q`

Text Solution

AI Generated Solution

The correct Answer is:
To convert the statement "it is wrong that he is intelligent or strong" into symbolic form, we can follow these steps: ### Step-by-Step Solution: 1. **Identify the Statements:** - Let \( p \) represent "He is intelligent." - Let \( q \) represent "He is strong." 2. **Understand the Phrase "It is wrong that":** - The phrase "it is wrong that" indicates negation. In logical terms, this can be represented by the symbol \( \neg \) (not). 3. **Translate "or" into Logical Symbols:** - The word "or" in logic is represented by the symbol \( \lor \) (disjunction). Therefore, "He is intelligent or strong" can be represented as \( p \lor q \). 4. **Combine the Parts:** - The entire statement "it is wrong that he is intelligent or strong" can be expressed as the negation of the disjunction: \[ \neg (p \lor q) \] 5. **Apply De Morgan's Law:** - According to De Morgan's Law, the negation of a disjunction can be expressed as the conjunction of the negations: \[ \neg (p \lor q) = \neg p \land \neg q \] This means "He is not intelligent and he is not strong." ### Final Symbolic Form: Thus, the symbolic form of the statement "it is wrong that he is intelligent or strong" is: \[ \neg p \land \neg q \]

To convert the statement "it is wrong that he is intelligent or strong" into symbolic form, we can follow these steps: ### Step-by-Step Solution: 1. **Identify the Statements:** - Let \( p \) represent "He is intelligent." - Let \( q \) represent "He is strong." ...
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