let p: the kitchen is clean. let q: the bedroom is clean. which statement is true if the kitchen is clean…

let p: the kitchen is clean. let q: the bedroom is clean. which statement is true if the kitchen is clean but the bedroom is not clean? if p is true, then q is true. statement q is true if and only if p is true. both p and q are true. statement p or q is true.

let p: the kitchen is clean. let q: the bedroom is clean. which statement is true if the kitchen is clean but the bedroom is not clean? if p is true, then q is true. statement q is true if and only if p is true. both p and q are true. statement p or q is true.

Answer

Explanation:

Step1: Analyze given conditions

Given $p$ (kitchen is clean) is true and $q$ (bedroom is clean) is false.

Step2: Evaluate each option

  • Option 1: “If $p$ is true, then $q$ is true.” Since $p$ is true but $q$ is false, this is false.
  • Option 2: “Statement $q$ is true if and only if $p$ is true.” $q$ is false and $p$ is true, so this is false.
  • Option 3: “Both $p$ and $q$ are true.” $q$ is false, so this is false.
  • Option 4: “Statement $p$ or $q$ is true.” In logic, for $p\vee q$, if at least one of $p$ or $q$ is true, the statement is true. Since $p$ is true, $p\vee q$ is true.

Answer:

Statement $p$ or $q$ is true.