Proof & Structure: Solve (¬ p V q) ↔ ( p Λ ¬ q) - John

In summary, the symbols ¬, V, Λ, and ↔ represent negation, disjunction, conjunction, and biconditional respectively in the given statement. The statement can be read as "Not p or q is true if and only if p and not q are both true." The purpose of the parentheses is to indicate the order of operations and group logical expressions. The logical structure of the statement is a biconditional statement. It can be proven to be true using logical equivalences and truth tables to show the equivalence of both sides.
  • #1
johnny009
7
0
Dear ALL,

Today, I am really struggling to complete...an important Assignment on time?

In particular, this Question has ...Frazzled me, re Truth Tables etc etc...?

Any good advice, by close of business - greatly appreciated.

----------------------------------------------------------------------------------------------------

Find the truth table of : (¬ p V q) ↔ ( p Λ ¬ q)
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Many Thanks

John.
 
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  • #2
P Q (¬p V q) (p Λ ¬q) (¬p V q) ↔ (p Λ ¬q)T T F F FT F T F FF T T F FF F T T T
 

FAQ: Proof & Structure: Solve (¬ p V q) ↔ ( p Λ ¬ q) - John

What is the meaning of the symbols ¬, V, Λ, and ↔ in the given statement?

The symbol ¬ represents negation, V represents disjunction, Λ represents conjunction, and ↔ represents biconditional (if and only if).

How do you read the given statement?

The statement can be read as "Not p or q is true if and only if p and not q are both true."

What is the purpose of the parentheses in the statement?

The parentheses are used to indicate the order of operations and to group together logical expressions.

What is the logical structure of the statement?

The logical structure of the statement is a biconditional statement, where both sides of the statement are equivalent.

How can this statement be proven to be true?

The statement can be proven to be true using logical equivalences and truth tables to show that both sides of the statement are equivalent.

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