Consider the following sentence: If the Standard Model of particle physics is va
ID: 3643784 • Letter: C
Question
Consider the following sentence:If the Standard Model of particle physics is valid, then neutrinos have zero mass and travel at the speed of light.
a. Identify the primitive statements in this sentence (those that cannot be decomposed into simpler parts connected by logical connectives), and assign variable names to them.
b. Write the statement symbolically, using the variable names you chose.
c. Write the symbolic negation of your answer in (b), then simplify it by applying all applicable negation rules.
d. Translate your answer to part (c) into clear, grammatically correct English.
Explanation / Answer
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a) Primitive statements:
1) Standard model of particle physics is valid ( let this be denoted by 'P' )
2) neutrinos have zero mass ( let this be denoted by 'M' )
3) neutrinos travel at speed of light ( let this be denoted by 'S' )
b) P => ( M ^ S ) [ ^ denotes logical 'and' and '=>' denotes implication ]
c) ! ( P => ( M ^ S ) ) [ ! denotes logical not ]
we know that ! ( P => Q ) = P ^ !Q
So ! ( P => ( M ^ S ) ) = P ^ ! ( M ^ S)
Applying demorgans law
= P ^ ( !M v !S ) [ v denotes logical or ]
d) Translating into English we have " The standard model of particle physics is valid and neutrons have non zero mass or do not travel with speed of light "