Q: How do you rewrite a biconditional as two conditional statements?

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If lines lie in two planes, then the lines are coplanar.

A bi-conditional statement is one which says that if any one of two statements is true, the other is true, too. It generally takes the form, X is true if and only if Y is true, or X is equivalent to Y, where X and Y are simpler statements.

No, not always. It depends on if the original biconditional statement is true. For example take the following biconditional statement:x = 3 if and only if x2 = 9.From this biconditional statement we can extract two conditional statements (hence why it is called a bicondional statement):The Conditional Statement: If x = 3 then x2 = 9.This statement is true. However, the second statement we can extract is called the converse.The Converse: If x2=9 then x = 3.This statement is false, because x could also equal -3. Since this is false, it makes the entire original biconditional statement false.All it takes to prove that a statement is false is one counterexample.

Two figures are congruent if and only if they have the same shape and size.

There are two statements and it is not clear which one you are referring to.

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A biconditional statement is a compound statement consisting of a double conditional: "She's going to the party if and only if I'm going." (I'm going if she's going and vice-versa.) Thus, it's basically the conjunction of two conditionals, where the antecedent of either is the consequent of the other.

If lines lie in two planes, then the lines are coplanar.

A bi-conditional statement is one which says that if any one of two statements is true, the other is true, too. It generally takes the form, X is true if and only if Y is true, or X is equivalent to Y, where X and Y are simpler statements.

No, not always. It depends on if the original biconditional statement is true. For example take the following biconditional statement:x = 3 if and only if x2 = 9.From this biconditional statement we can extract two conditional statements (hence why it is called a bicondional statement):The Conditional Statement: If x = 3 then x2 = 9.This statement is true. However, the second statement we can extract is called the converse.The Converse: If x2=9 then x = 3.This statement is false, because x could also equal -3. Since this is false, it makes the entire original biconditional statement false.All it takes to prove that a statement is false is one counterexample.

A biconditional is a statement wherein the truth of each item depends on the truth of the other.

Two figures are congruent if and only if they have the same shape and size.

Disjunction

If two numbers are reciprocals, then their product is 1. If the product of two numbers is 1, then they are reciprocals.

#include<stdio.h> void main() { int a=10,b=15; clrscr(); if(a>b) printf("%d is the large number",a); else printf("%d is the large number",b); getch(); }

The law of syllogism is a logical rule that lets you draw a conclusion from two conditional statements. If the first statement leads to the second statement and the second statement leads to a third statement, you can infer that the first statement leads to the third statement. It's a way to combine multiple conditional statements to draw a single conclusion.

There are two statements and it is not clear which one you are referring to.

the product of two integers is odd if and only if the two factors are odd