What is the symbolic form of the statement 'It is not true that both the cat and the dog are outside'?
Understand the Problem
The question is asking for the symbolic representation of a logical statement involving two subjects: a cat and a dog. The statement focuses on the negation of the scenario where both are outside.
Answer
¬(C ∧ D)
The symbolic form is ¬(C ∧ D), using De Morgan's laws.
Answer for screen readers
The symbolic form is ¬(C ∧ D), using De Morgan's laws.
More Information
This statement uses logical connectives. The conjunction 'and' is represented by '∧', while the negation 'not' is represented by '¬'. This structure emphasizes that it is not true for both the cat (C) and the dog (D) to be outside simultaneously.
Tips
A common mistake is reversing the symbols or misunderstanding the scope of the negation. De Morgan's laws clarify that negating a conjunction involves negating the entire statement.
Sources
- 1.1.3: Compound Statements - Mathematics LibreTexts - math.libretexts.org
