Exam 11: Predicate Logic

In the following proof, which justification is correct for line 7? \begin{array}{llcc} \text { (1) (\exists x) \mathrm{L} x \supset(x)(\mathrm{M} x \supset \mathrm{N} x) } && \text {Premise } \\ \text { (2) \( \mathrm{Lb} \cdot \mathrm{Mb} \) } & \text { \(/ \mathrm{Nb}\) } & \text { Premise/Conclusion }\\ \text { (3) \( \mathrm{Lb} \)} && \text { 2 simp }\\ \text { (4) \( (\exists x) \mathrm{L} x \) } && \text { \( 3 \mathrm{EG} \) }\\ \text { (5) \( (x)(\mathrm{M} x \supset \mathrm{N} x) \) } && \text { 1, \( 4 \mathrm{MP} \) }\\ \text { (6) \( \mathrm{Mb} D \mathrm{Nb} \) } && \text { \( 5 \mathrm{UI} \) }\\ \text { (7) \( \mathrm{Mb} \) } & \end{array}

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

Symbolize the following statement. Joan loves Henry and Henry loves Joan.

In the following proof, which justification is correct for line 6? \begin{array}{llcc} \text { (1) (z)(\mathrm{I} z \cdot \mathrm{Tz}) } && \text {Premise } \\ \text { (2) (?y) \( \mathrm{Iy} \supset(\exists z) \mathrm{Hz} \)} & \text { \(/(\exists z) \mathrm{T} z \cdot(\exists z) \mathrm{Hz}\) }& \text { Premise/Conclusion }\\ \text { (3) \( \mathrm{Ia} \cdot \mathrm{Ta} \) } &&1 \mathrm{UI} \\ \text { (4) \( \mathrm{Ia} \) } && 3 \mathrm{Simp}\\ \text { \(\text { (5) (?y) } I y\) } && 4 \mathrm{EG}\\ \text {(6) \( (\exists z) \mathrm{Hz} \) } &\\\end{array}

Identify the quantity and quality of the following statement form. Not a single S is P.

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

In the following proof, which justification is correct for line 4? (1) Mnn \cdot \sim Enr Premise (2) (\existsz)\sim(z\supsetz)\supset(x)xx / Premise/Conclusion (3) \sim( Mnn -\sim Enr ) 1 (4) \sim (Mnn \supset Enr)

The statement ~[( $\exists$ x)Px $\bigvee$ ( $\exists$ x)Qx] is which kind of statement?

Translate the following symbolized categorical statement into English using the provided key. $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\mathrm{B} x=x \text { is a badger } \quad \mathrm{M} x=x \text { is mortal }$ $(x)(\mathrm{B} x \supset \mathrm{M} x)$

The statement Za $\supset$ ~Wa is which kind of statement?

Identify the quantity and quality of the following statement form. Some football players are business majors.

( $\exists$ z)Nz is called a(n) _____ sentence and the variable z is said to be _____.

Symbolize the following statement form. All A are B.

The following inference is an application of which rule? ~(x)~(y)( $\exists$ z)Rxyz.Therefore, ( $\exists$ x)(y)( $\exists$ z)Rxyz.

Symbolize the following statement. Some cruise ships do not stop at any islands.

The statement Ab $\bigvee$ Cb is which kind of statement?

Symbolize the following statement. Every psychiatrist is a medical doctor.

The following inference is an application of which rule? (Mj • Bj) $\equiv$ Dj.Therefore, ( $\exists$ x)[(Mx • Bj) $\equiv$ Dj].

Symbolize the following statement. Many of the transcendentalists came from New England.

In the following proof, which justification is correct for line 3? \begin{array}{llcc} \text {(1) (x)[(\mathrm{C} x \cdot \mathrm{D} x) \supset \sim \mathrm{E} x] } & & \text { Premise } \\ \text { (2) \( \mathrm{Eb} \) } & \text {\(I \sim \mathrm{Cb} \cup \sim \mathrm{Db}\) }& \text { Premise/C onclusi on }\\ \text { (3) \( (\mathrm{Cb} \cdot \mathrm{Db}) \supset \sim \mathrm{Eb} \) } &\\\end{array}