Problem_Set_5_solutions

# Problem_Set_5_solutions - quantifier, so we cant add...

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V83.0070 Logic Spring 2008 Matt Kotzen Problem Set 5 Solutions 7.3E: 2b) Bct 2d) Bds 2f) (( Bak Bbk) ( Bck Bdk)) Bek 2h) Atp Ath 2j) Lbp Ldp 2l) (Tbc Tca) ( Tbe & Tce) 2n) ((Tab & Tac) (Tad Tae)) 2p) Tcb Aca 7.4E: 1b) ( x)Bx 1d) ( x) Bx 1f) ( x)Bx ( x)Rx 1h) ( x)Bx ( x)Rx 1j) ( x)Bx ( x)Rx 3b) ( x)Px Pj 3d) ( x)Px Pr 3f) ( x)Px ( x)Px 3h) ( Pj ( x)Px) (Pj ( x)Px) 3j) ( x)Sx ( x)Px 7.5E: 1b) No. “(x)” is missing a quantifier. 1d) No. “ ” is the existential quantifier, not “E” 1f) No. “Faa” doesn’t have any unbound x’s. 1h) No. The x’s in “Px” and “Gx” were already within the scope of the universal

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Unformatted text preview: quantifier, so we cant add another x-quantifier 1j) Yes. Sentence, since all variables are bound. 1l) Yes. Sentence, since all variables are bound. 1n) No. Quantifiers have to range over variables, not constants. 1p) No. The z in Gaz was already bound by the existential quantifier, so we cant add another z-quantifier. 7.7E: 2b) ( x)(Lx Fx) 2d) ( x)(Lx &amp; Cxd) 2f) ( x)((Lx &amp; Fx) Bx) 2h) ( x)(Lx &amp; Cxd) &amp; ( x)(Tx &amp; Cxd) 2j) ( x)[((Lx Tx) &amp; Fx) Bx] 2l) Bd &amp; ( x)[((Fx&amp;Lx) (Fx&amp;Tx)) Bx] 2n) ( x)(Lx (Fx Cdx)) 2p) Fd ( x)(Lx Tx)...
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## Problem_Set_5_solutions - quantifier, so we cant add...

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