Question

Choose the correct translation of the following statement into symbolic form using the uppercase letters available. If neither water nor soft drinks can quench your thirst, then juice will not do it, unless the juice contains electrolytes. Let W = water can quench your thirst, S = soft drinks can quench your thirst, J = juice will quench your thirst, and E= the juice contains electrolytes a)-(WvS)-(-VE) b) - (WvS) (-) El c)-(WvS) (-JVE) d) - (Wv 5)(-). E) Question 16 (1 point) Choose the correct translation of the following statement into symbolic form using the uppercase letters available. If the dryer breaks, then we will hang the clothes to dry, or take the clothes to a coin-operated laundry. Let D = the dryer breaks, B = we will hang the clothes to dry, and C = we will take the clothes to a coin-operated laundry a) (DB) b)(DVB) vc c) CV (DB) d) DBVC Question 17 (1 point) If " X is true, then what is X? a) X is true. b) Xis false. c) X could be true or false. Question 18 (1 point) If "Xv Y is false, then can one of the disjuncts be true? a) Yes O b) No

Answer 1

Answer:

¬(W∨S)→¬(J∨E)

D→(B∨C)

X is true

No

Step-by-step explanation:

The hypotheses  "neither water nor soft drinks can quench your thirst" translates to ¬(W∨S) ("neither nor" negates the disjunction W∨S). The "if,... then" translates to the implication symbol (arrow). The conclusion "juice will not do it, unless the juice contains electrolytes" translates to ¬(J∨E). This is because if J or E were true, then J would be true (because E implies J), contrary to the conclusion that J is false ("juice will not do it"), then J∨S is false.

The hypothesis here is "the dyer breaks" hence D is the hypothesis. The conclusion is "we will hang the clothes to dry, or take the clothes to a coin-operated laundry" which is the same as (B∨C).

The proposition p→p is always true (according to truth tables). In this case, p:=X is true, then p is true and X is true.

X∨Y is false if and only if X is false and Y is false, so both statements X,Y must be false.