First time here? Checkout the FAQ!
+4 votes

The CORRECT formula for the sentence, "not all Rainy days are Cold" is

  1. $\forall d (\text{Rainy}(d) \wedge \text{~Cold}(d))$
  2. $\forall d ( \text{~Rainy}(d) \to \text{Cold}(d))$
  3. $\exists d(\text{~Rainy}(d) \to \text{Cold}(d))$
  4. $\exists d(\text{Rainy}(d) \wedge \text{~Cold}(d))$
asked in Mathematical Logic by Veteran (75.6k points)  
edited by | 565 views
Is there typo in last option ? please correct it !

4 Answers

+10 votes
Best answer

Not all rainy days are cold.

In other words it says "Some rainy days are cold" or "Some rainy days are not cold"

Given statement is

<=> ∃ d[R(d) ^ ~C(d)]


answered by Loyal (3.3k points)  
selected by
+14 votes
A) No rainy days are cold

B) All non-rainy days are cold

C)Some non-rainy days are cold.

D) Some rainy days are not cold.

option D
answered by Loyal (2.8k points)  
Is option (A) statement correct?
Statement A  shoud be "all days are rainy days and they are not cold "
+2 votes

not all rainy days are cold : meaning "there are some rainy days which are cold" = "some days are rainy and not cold".

∃d{R(d) \scriptstyle \wedge ¬C(d)}


ans = option D

answered by Veteran (27.5k points)  
0 votes

(A)∀d(R(d)⋀~C(d)) = d(~(~R(d) V C(d))) (taking negation common)

                                   =∀d(~(R(d)->C(d)))= All days are not Rainy days and also are not Cold

(B)d(~R(d)->C(d))=The day which are not Rainy day are Cold

(C)∃d(~R(d)->C(d))=∃d(R(d)VC(d))=Some day are Rainy days or some days are Cold

(D)∃d(R(d)⋀~C(d))= Some Rainy days are not Cold

                                = ~ (∀d(R(d)->C(d))) (taking negation common)

                                =not all Rainy days are Cold

answered by Veteran (51.7k points)  
edited by
Top Users Feb 2017
  1. Arjun

    5288 Points

  2. Bikram

    4230 Points

  3. Habibkhan

    3952 Points

  4. Aboveallplayer

    3086 Points

  5. Debashish Deka

    2378 Points

  6. sriv_shubham

    2308 Points

  7. Smriti012

    2236 Points

  8. Arnabi

    2008 Points

  9. mcjoshi

    1690 Points

  10. sh!va

    1684 Points

Monthly Topper: Rs. 500 gift card

20,860 questions
26,012 answers
22,114 users