Answer :
To solve this problem, we need to identify pairs of statements that can form a biconditional. A biconditional is where both parts are reversible, meaning if one statement is true, the other must also be true, and vice versa. Let's break it down step-by-step:
1. Understand the statements:
- Let's analyze each statement to understand what relationships they express.
- The statement "If A, then B" can form a biconditional with "If B, then A."
2. Analyze each statement:
- Statement 1: If [tex]\(4s-7=-8\)[/tex], then [tex]\(4t-2=10\)[/tex].
- Statement 2: If [tex]\(4s-8=-7\)[/tex], then [tex]\(10t+4=-2\)[/tex].
- Statement 3: If [tex]\(4t+10=-2\)[/tex], then [tex]\(4s-8=-7\)[/tex].
- Statement 4: If [tex]\(10t+4=-2\)[/tex], then [tex]\(4s=-7\)[/tex].
- Statement 5: If [tex]\(4t-2=10\)[/tex], then [tex]\(4s-7=-8\)[/tex].
- Statement 6: If [tex]\(4s=-7\)[/tex], then [tex]\(4t+10=-2\)[/tex].
3. Identify pairs for biconditional:
- We need to find pairs where the implication works both ways.
- Pair 1:
- Statement 1 and Statement 5:
- Statement 1: If [tex]\(4s-7=-8\)[/tex], then [tex]\(4t-2=10\)[/tex].
- Statement 5: If [tex]\(4t-2=10\)[/tex], then [tex]\(4s-7=-8\)[/tex].
- These two statements are reversible, meaning they form a biconditional: [tex]\(4s-7=-8\)[/tex] if and only if [tex]\(4t-2=10\)[/tex].
- Pair 2:
- Statement 3 and Statement 6:
- Statement 3: If [tex]\(4t+10=-2\)[/tex], then [tex]\(4s-8=-7\)[/tex].
- Statement 6: If [tex]\(4s=-7\)[/tex], then [tex]\(4t+10=-2\)[/tex].
- These two statements are reversible, meaning they form a biconditional: [tex]\(4t+10=-2\)[/tex] if and only if [tex]\(4s=-7\)[/tex].
Each of these pairs represents two statements that can form a biconditional. Therefore, the selected biconditional statements are:
- Pair 1: "If [tex]\(4s-7=-8\)[/tex], then [tex]\(4t-2=10\)[/tex]" and "If [tex]\(4t-2=10\)[/tex], then [tex]\(4s-7=-8\)[/tex]."
- Pair 2: "If [tex]\(4t+10=-2\)[/tex], then [tex]\(4s-8=-7\)[/tex]" and "If [tex]\(4s=-7\)[/tex], then [tex]\(4t+10=-2\)[/tex]."
1. Understand the statements:
- Let's analyze each statement to understand what relationships they express.
- The statement "If A, then B" can form a biconditional with "If B, then A."
2. Analyze each statement:
- Statement 1: If [tex]\(4s-7=-8\)[/tex], then [tex]\(4t-2=10\)[/tex].
- Statement 2: If [tex]\(4s-8=-7\)[/tex], then [tex]\(10t+4=-2\)[/tex].
- Statement 3: If [tex]\(4t+10=-2\)[/tex], then [tex]\(4s-8=-7\)[/tex].
- Statement 4: If [tex]\(10t+4=-2\)[/tex], then [tex]\(4s=-7\)[/tex].
- Statement 5: If [tex]\(4t-2=10\)[/tex], then [tex]\(4s-7=-8\)[/tex].
- Statement 6: If [tex]\(4s=-7\)[/tex], then [tex]\(4t+10=-2\)[/tex].
3. Identify pairs for biconditional:
- We need to find pairs where the implication works both ways.
- Pair 1:
- Statement 1 and Statement 5:
- Statement 1: If [tex]\(4s-7=-8\)[/tex], then [tex]\(4t-2=10\)[/tex].
- Statement 5: If [tex]\(4t-2=10\)[/tex], then [tex]\(4s-7=-8\)[/tex].
- These two statements are reversible, meaning they form a biconditional: [tex]\(4s-7=-8\)[/tex] if and only if [tex]\(4t-2=10\)[/tex].
- Pair 2:
- Statement 3 and Statement 6:
- Statement 3: If [tex]\(4t+10=-2\)[/tex], then [tex]\(4s-8=-7\)[/tex].
- Statement 6: If [tex]\(4s=-7\)[/tex], then [tex]\(4t+10=-2\)[/tex].
- These two statements are reversible, meaning they form a biconditional: [tex]\(4t+10=-2\)[/tex] if and only if [tex]\(4s=-7\)[/tex].
Each of these pairs represents two statements that can form a biconditional. Therefore, the selected biconditional statements are:
- Pair 1: "If [tex]\(4s-7=-8\)[/tex], then [tex]\(4t-2=10\)[/tex]" and "If [tex]\(4t-2=10\)[/tex], then [tex]\(4s-7=-8\)[/tex]."
- Pair 2: "If [tex]\(4t+10=-2\)[/tex], then [tex]\(4s-8=-7\)[/tex]" and "If [tex]\(4s=-7\)[/tex], then [tex]\(4t+10=-2\)[/tex]."
