A. Each of the following sentences is ambiguous. Provide a symbolization key for each, and symbolize all readings.

1. 1.
   ​

   No one likes a quitter.

   domain:

   people

   $Q(x)$:

   blank _x is a quitter

   $L(x,y)$:

   blank _x likes blank _y

2. $\forall x(Q(x)\to \forall y\neg L(y,x))$ (all quitters are disliked by everyone)
   $\exists x(Q(x)\wedge \forall y\neg L(y,x))$ (A specific quitter is disliked by everyone)

3. 2.
   ​

   CSI found only red hair at the scene.

   domain:

   items of evidence

   $R(x)$:

   blank _x is red

   $H(x)$:

   blank _x is hair

   $F(x,y)$:

   blank _x found blank _y (at the scene)

   $c$:

   CSI

4. $\forall x(F(c,x)\to (R(x)\wedge H(x)))$ (only hair was found, and it’s all red)
   $\forall x((F(c,x)\wedge H(x))\to R(x))$ (only red hair was found, but possibly other things that aren’t hair)

5. 3.
   ​

   Smith’s murderer hasn’t been arrested.

   domain:

   people

   $A(x)$:

   blank _x has been arrested

   $M(x,y)$:

   blank _x murdered blank _y

   $m$:

   Smith

6. $\exists x(\forall y(M(y,m)\leftrightarrow y=x)\wedge \neg A(x))$ (Smith’s murderer has: not been arrested)
   $\neg \exists x(\forall y(M(y,m)\leftrightarrow y=x)\wedge A(x))$ (It’s not the case that Smith’s murderer has been arrested; in fact there may not be a “Smith’s murderer”.)