Match the English Statement with All Its Equivalent Symbolic Statements $\exists x \forall y T ( x , y )$

question 43

Short Answer

Match the English statement with all its equivalent symbolic statements in this list: 1. $\exists x \forall y T ( x , y )$$\quad$$\quad$$\quad$ 2. $\exists y \forall x T ( x , y )$$\quad$$\quad$$\quad$ 3. $\forall x \exists y T ( x , y )$
4. $\neg \exists x \exists y T ( x , y )$$\quad$$\quad$ 5. $\exists x \forall y \neg T ( x , y )$$\quad$$\quad$$\quad$ 6. $\forall y \exists x T ( x , y )$
7. $\exists y \forall x \neg T ( x , y )$$\quad$$\quad$ 8. $\neg \forall x \exists y T ( x , y )$$\quad$$\quad$$\quad$ 9. $\neg \exists y \forall x T ( x , y )$
10. $\neg \forall x \exists y \neg T ( x , y )$$\quad$ 11. $\neg \forall x \neg \forall y \neg T ( x , y )$$\quad$ 12. $\forall x \exists y \neg T ( x , y )$
-Some students are taking no courses.

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Definitions:

Philosophical Idea

A concept or thought derived from philosophical inquiry, relating to fundamental questions about life, existence, knowledge, values, reason, and reality.

Existential

Relating to existentialism, a philosophical theory focusing on individual freedom, choice, and existence.

Evaluating

The process of determining the significance, worth, or condition of something, typically following an analysis of its attributes.

Conditions of Worth

Standards and expectations imposed by others that one feels they must meet to be valued and accepted.