Exam 11: Predicate Logic

Symbolize the following statement. Joan loves someone or someone loves Joan.

Symbolize the following statement. All objects that have mass have a specifiable quantity of matter.

Identify the quantity and quality of the following statement form. Any S is P.

Symbolize the following statement. No buildings in Iceland are air-conditioned.

The statement ( $\exists$ x)Fx is which kind of statement?

Symbolize the following statement. Some sporting events do not create great revenues.

Symbolize the following statement. Some people eat three meals a day, but I don't.

Translate the following symbolized categorical statement into English using the provided key. Lx =x is a human language Mx= x is modality-independent (x)(Lx $\supset$ Mx)

Identify the quantity and quality of the following statement. ( $\exists$ x)(Fx • Gx)

Translate the following symbolized categorical statement into English using the provided key. W $x = x$ was a wife of King Henry VIII $\quad \mathrm { B } x = x$ lived beyond 30 years of age $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$( \exists x ) ( \mathrm { W } x \cdot \sim \mathrm { B } x )$

The statement (x)Lx is which kind of statement?

Identify the type of statement represented by the following. Px

The following inference is an application of which rule? (z)~(Pz • Qa).Therefore, ~( $\exists$ z)(Pz • Qa).

Symbolize the following statement. Not all books are well written.

In the following proof, which justification is correct for line 11? \begin{array}{llcc} \text { (1) (x)[\mathrm{G} x \supset(y)(\mathrm{H} y \supset \mathrm{I} x y)] } && \text {Premis} \\ \text {(2) \( (\exists x)[\mathrm{G} x \cdot(\exists y) \sim \mathrm{I} x y] \) } &\text { \(I \sim(x) \mathrm{H} x\) }&\text {Premise/Conclusion} \\ \text { (3) \( (x) \mathrm{H} x \) } && \text {Assumption}\\ \text {(4) \( \mathrm{Ga} \cdot(\exists y) \sim \mathrm{Iay} \) } && \text {\( 2 \mathrm{EI} \)}\\ \text {(5) \( \mathrm{Ga} \) } && \text {\( 4 \operatorname{Sinp} \)}\\ \text { (6) ( \( \exists y) \sim \) Iay } && \text {\( 4 \operatorname{Sinp} \)}\\ \text { (7) \( -\mathrm{Iab} \) } & & \text {\( 6 \mathrm{EI} \)} \\ \text {(8) \( \mathrm{Ga} \supset(\mathrm{y})(\mathrm{Hy} \supset \mathrm{Iay}) \) } && \text {\( 1 \mathrm{UI} \)}\\ \text { (9) \( (\mathrm{y})(\mathrm{Hy} \supset \mathrm{Iay}) \) } && \text {\( 5,8 \mathrm{MP} \)}\\ \text {(10) \( \mathrm{Hb} \supset \mathrm{Iab} \) } &&\text {\( 9 \mathrm{UI} \)}\\ \text { (11) \( \mathrm{Hb} \) } &\\ &\\\end{array}

In the following proof, which justification is correct for line 3? \begin{array}{llcc} \text { (1) (x)[(\mathrm{C} x * \sim \mathrm{D} x) \supset \mathrm{E} x] } & & \text {Premise } \\ \text { (2) \( (x)(\mathrm{E} x \supset \mathrm{D} x) \)} & \text { \(/(x)(C x \supset D x)\)}& \text { Premise/Conclusion } \\ \text {(3) \( \mathrm{Ca} \) } &\\\end{array}

~(x)Nz is called a(n) _____ sentence and the variable z is said to be _____.

Translate the following symbolized categorical statement into English using the provided key. $\mathrm { A } x = x$ is an avocado tree $\quad$$\quad$$\mathrm { C } x = x$ grows in California $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$( \exists x ) ( \mathrm { Ax } \cdot \mathrm { C } x )$

The following inference is an application of which rule? Ca.Therefore, ( $\exists$ x)Cx.

Identify the quantity and quality of the following statement form. Some colleges do not have entrance requirements.