Symbolic translation of negations, conjunctions, and disjunctions:... Consider statements \( p \) and \( q \). \( p \) : It is snowing. \( q \) : We are going sledding. For parts (a) and (b), fill in the symbolic form. For part (c), choose the descriptive form. Descriptive form Symbolic form (a) We are going sledding or it is not snowing. (b) It is not snowing or we are not going sledding. \( \square \) (c) \( \square \) (Choose one) \[ \sim(q \wedge p) \] It is not the case that "it is snowing or we are going sledding". \( \square \) We are going sledding and it is snowing. Explanatic It is not the case that "we are going sledding and it is snowing".

We can fill in the blanks with the right symbolic forms and interpret their meanings in a fun way! For part (a), the statement "We are going sledding or it is not snowing" can be expressed as \( q \vee \sim p \). This means that either we jump on those sleds, or we're enjoying the sight of fluffy snowflakes falling. For part (b), "It is not snowing or we are not going sledding" translates to \( \sim p \vee \sim q \). Here, we’re saying that either the snow is just a myth, or we might be staying inside, perhaps sipping hot cocoa! For part (c), for the description you provided, the symbolic form is \( \sim(q \wedge p) \). We could say: "It's simply not true that both we're going sledding and it's snowing—there's always an adventure out there!"