[amp_mcq option1=”None follows” option2=”Only either I or II follows” option3=”Only II follows” option4=”Only I and III follow E. None of these” correct=”option3″]<\/p>\n
The correct answer is $\\boxed{\\text{A. None follows}}$.<\/p>\n
The first statement, “Some towels are brushes,” can be expressed in propositional logic as $\\exists x(T(x) \\land B(x))$. The second statement, “No brush is soap,” can be expressed as $\\forall x(B(x) \\rightarrow \\neg S(x))$. The third statement, “All soaps are rats,” can be expressed as $\\forall x(S(x) \\rightarrow R(x))$.<\/p>\n
The first conclusion, “Some rats are brushes,” can be expressed as $\\exists x(R(x) \\land B(x))$. This conclusion does not follow from the premises, because the premises do not tell us anything about whether or not there are any rats.<\/p>\n
The second conclusion, “No rat is brush,” can be expressed as $\\forall x(R(x) \\rightarrow \\neg B(x))$. This conclusion also does not follow from the premises, because the premises do not tell us anything about whether or not there are any rats.<\/p>\n
The third conclusion, “Some towels are soaps,” can be expressed as $\\exists x(T(x) \\land S(x))$. This conclusion also does not follow from the premises, because the premises do not tell us anything about whether or not there are any towels.<\/p>\n
Therefore, none of the conclusions follow from the premises.<\/p>\n","protected":false},"excerpt":{"rendered":"
[amp_mcq option1=”None follows” option2=”Only either I or II follows” option3=”Only II follows” option4=”Only I and III follow E. None of these” correct=”option3″]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[723],"tags":[],"class_list":["post-50480","post","type-post","status-publish","format-standard","hentry","category-logical-deduction","no-featured-image-padding"],"yoast_head":"\n